Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
url
stringclasses
147 values
commit
stringclasses
147 values
file_path
stringlengths
7
101
full_name
stringlengths
1
94
start
stringlengths
6
10
end
stringlengths
6
11
tactic
stringlengths
1
11.2k
state_before
stringlengths
3
2.09M
state_after
stringlengths
6
2.09M
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
rw [Nat.add_assoc]
case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ Nat.succ 0 < 1 + sizeOf l✝ + sizeOf r✝
case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
apply Nat.lt_add_of_pos_right
case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
first | (apply Nat.add_pos_left; apply sizeOf_pos) | (apply Nat.add_pos_right; apply sizeOf_pos)
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
(apply Nat.add_pos_left; apply sizeOf_pos)
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
apply Nat.add_pos_left
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
apply sizeOf_pos
case mp.semiL.h.h P✝ : Sort u_1 b : Bunch P✝ l✝ : BunchWithHole P✝ r✝ : Bunch P✝ h : (subst b l✝ ;ᡇ r✝) = b ⊒ 0 < sizeOf l✝
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
(apply Nat.add_pos_right; apply sizeOf_pos)
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
apply Nat.add_pos_right
case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf l✝ + sizeOf r✝
case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf r✝
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
apply sizeOf_pos
case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᡇ subst b r✝) = b ⊒ 0 < sizeOf r✝
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
rintro rfl
case mpr P✝ : Sort u_1 b : Bunch P✝ Ξ“ : BunchWithHole P✝ ⊒ Ξ“ = hole β†’ subst b Ξ“ = b
case mpr P✝ : Sort u_1 b : Bunch P✝ ⊒ subst b hole = b
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.subst_idem
[101, 9]
[116, 21]
simp
case mpr P✝ : Sort u_1 b : Bunch P✝ ⊒ subst b hole = b
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.idem_subst
[118, 9]
[120, 7]
rw [eq_comm]
P✝ : Sort u_1 b : Bunch P✝ Ξ“ : BunchWithHole P✝ ⊒ b = subst b Ξ“ ↔ Ξ“ = hole
P✝ : Sort u_1 b : Bunch P✝ Ξ“ : BunchWithHole P✝ ⊒ subst b Ξ“ = b ↔ Ξ“ = hole
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.idem_subst
[118, 9]
[120, 7]
simp
P✝ : Sort u_1 b : Bunch P✝ Ξ“ : BunchWithHole P✝ ⊒ subst b Ξ“ = b ↔ Ξ“ = hole
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.comp_hole
[148, 9]
[149, 30]
induction Ξ“ <;> simp_all
P : Sort u_1 Ξ“ : BunchWithHole P ⊒ Ξ“.comp hole = Ξ“
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.comp_def
[151, 1]
[153, 55]
induction h1 <;> simp_all [comp, FunLike.coe, subst]
P : Sort u_1 h1 h2 : BunchWithHole P b : Bunch P ⊒ ↑(h1.comp h2) b = ↑h1 (↑h2 b)
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_prop
[155, 9]
[157, 40]
cases Ξ“ <;> simp [FunLike.coe, subst]
P : Sort u_1 b : Bunch P Ο† : Typ P Ξ“ : BunchWithHole P ⊒ ↑Γ b = prop Ο† ↔ Ξ“ = hole ∧ b = prop Ο†
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.prop_eq
[159, 9]
[162, 7]
rw [show (prop Ο† = _ ↔ _ = prop Ο†) from ⟨Eq.symm, Eq.symm⟩]
P : Sort u_1 Ο† : Typ P b : Bunch P Ξ“ : BunchWithHole P ⊒ prop Ο† = ↑Γ b ↔ Ξ“ = hole ∧ b = prop Ο†
P : Sort u_1 Ο† : Typ P b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = prop Ο† ↔ Ξ“ = hole ∧ b = prop Ο†
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.prop_eq
[159, 9]
[162, 7]
simp
P : Sort u_1 Ο† : Typ P b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = prop Ο† ↔ Ξ“ = hole ∧ b = prop Ο†
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_cunit
[164, 9]
[166, 40]
cases Ξ“ <;> simp [FunLike.coe, subst]
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = cunit ↔ Ξ“ = hole ∧ b = cunit
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.cunit_eq
[168, 9]
[171, 7]
rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ cunit = ↑Γ b ↔ Ξ“ = hole ∧ b = cunit
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = cunit ↔ Ξ“ = hole ∧ b = cunit
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.cunit_eq
[168, 9]
[171, 7]
simp
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = cunit ↔ Ξ“ = hole ∧ b = cunit
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_sunit
[173, 9]
[175, 40]
cases Ξ“ <;> simp [FunLike.coe, subst]
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = sunit ↔ Ξ“ = hole ∧ b = sunit
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.sunit_eq
[177, 9]
[180, 7]
rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ sunit = ↑Γ b ↔ Ξ“ = hole ∧ b = sunit
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = sunit ↔ Ξ“ = hole ∧ b = sunit
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.sunit_eq
[177, 9]
[180, 7]
simp
P : Sort u_1 b : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = sunit ↔ Ξ“ = hole ∧ b = sunit
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_comma
[182, 1]
[188, 20]
cases Ξ“ <;> aesop
P : Sort u_1 b Δ₁ Ξ”β‚‚ : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = (Δ₁ ,ᡇ Ξ”β‚‚) ↔ Ξ“ = hole ∧ b = (Δ₁ ,ᡇ Ξ”β‚‚) ∨ (βˆƒ Ξ“', Ξ“ = commaL Ξ“' Ξ”β‚‚ ∧ ↑Γ' b = Δ₁) ∨ βˆƒ Ξ“', Ξ“ = commaR Δ₁ Ξ“' ∧ ↑Γ' b = Ξ”β‚‚
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_semi
[190, 1]
[196, 20]
cases Ξ“ <;> aesop
P : Sort u_1 b Δ₁ Ξ”β‚‚ : Bunch P Ξ“ : BunchWithHole P ⊒ ↑Γ b = (Δ₁ ;ᡇ Ξ”β‚‚) ↔ Ξ“ = hole ∧ b = (Δ₁ ;ᡇ Ξ”β‚‚) ∨ (βˆƒ Ξ“', Ξ“ = semiL Ξ“' Ξ”β‚‚ ∧ ↑Γ' b = Δ₁) ∨ βˆƒ Ξ“', Ξ“ = semiR Δ₁ Ξ“' ∧ ↑Γ' b = Ξ”β‚‚
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
intro h
P : Sort u_1 Ξ“ Ξ“' : BunchWithHole P Ο† Ο†' : Bunch P ⊒ ↑Γ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ Ξ“.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = Ξ“) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = Ξ“ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ξ“ Ξ“' : BunchWithHole P Ο† Ο†' : Bunch P h : ↑Γ Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ Ξ“.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = Ξ“) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = Ξ“ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
induction Ξ“ generalizing Ξ“'
P : Sort u_1 Ξ“ Ξ“' : BunchWithHole P Ο† Ο†' : Bunch P h : ↑Γ Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ Ξ“.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = Ξ“) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = Ξ“ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
case hole P : Sort u_1 Ο† Ο†' : Bunch P Ξ“' : BunchWithHole P h : ↑hole Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ hole.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = hole) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = hole ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case commaL P : Sort u_1 Ο† Ο†' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : βˆ€ {Ξ“' : BunchWithHole P}, ↑l✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ l✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = l✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = l✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑(commaL l✝ r✝) Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (commaL l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = commaL l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = commaL l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case commaR P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑(commaR l✝ r✝) Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (commaR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = commaR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = commaR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case semiL P : Sort u_1 Ο† Ο†' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : βˆ€ {Ξ“' : BunchWithHole P}, ↑l✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ l✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = l✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = l✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑(semiL l✝ r✝) Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiL l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiL l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiL l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case semiR P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑(semiR l✝ r✝) Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
case hole => simp_all
P : Sort u_1 Ο† Ο†' : Bunch P Ξ“' : BunchWithHole P h : ↑hole Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ hole.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = hole) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = hole ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp_all
P : Sort u_1 Ο† Ο†' : Bunch P Ξ“' : BunchWithHole P h : ↑hole Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ hole.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = hole) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = hole ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑(semiR l✝ r✝) Ο† = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : (l✝ ;ᡇ ↑r✝ Ο†) = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rw [eq_comm] at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : (l✝ ;ᡇ ↑r✝ Ο†) = ↑Γ' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑Γ' Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
first | rw [eq_comma] at h | rw [eq_semi] at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑Γ' Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : Ξ“' = hole ∧ Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ∨ (βˆƒ Ξ“'_1, Ξ“' = semiL Ξ“'_1 (↑r✝ Ο†) ∧ ↑Γ'_1 Ο†' = l✝) ∨ βˆƒ Ξ“'_1, Ξ“' = semiR l✝ Ξ“'_1 ∧ ↑Γ'_1 Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rcases h with (⟨rfl,rfl⟩|βŸ¨Ξ“'',rfl,h⟩|βŸ¨Ξ“'',rfl,h⟩)
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : Ξ“' = hole ∧ Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ∨ (βˆƒ Ξ“'_1, Ξ“' = semiL Ξ“'_1 (↑r✝ Ο†) ∧ ↑Γ'_1 Ο†' = l✝) ∨ βˆƒ Ξ“'_1, Ξ“' = semiR l✝ Ξ“'_1 ∧ ↑Γ'_1 Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
case inl.intro P : Sort u_1 Ο† l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' (l✝ ;ᡇ ↑r✝ Ο†) β†’ (βˆƒ Ξ”, Ο† = ↑Δ (l✝ ;ᡇ ↑r✝ Ο†) ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, (l✝ ;ᡇ ↑r✝ Ο†) = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' (l✝ ;ᡇ ↑r✝ Ο†) = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ (l✝ ;ᡇ ↑r✝ Ο†) ∧ (semiR l✝ r✝).comp Ξ” = hole) ∨ (βˆƒ Ξ”, (l✝ ;ᡇ ↑r✝ Ο†) = ↑Δ Ο† ∧ hole.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = hole ∧ Ξ”' (l✝ ;ᡇ ↑r✝ Ο†) = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case inr.inl.intro.intro P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = l✝ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = semiL Ξ“'' (↑r✝ Ο†)) ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiL Ξ“'' (↑r✝ Ο†)).comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ case inr.inr.intro.intro P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = semiR l✝ Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiR l✝ Ξ“'').comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiR l✝ Ξ“'' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rw [eq_comma] at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑Γ' Ο†' = (l✝ ,ᡇ ↑r✝ Ο†) ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (commaR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = commaR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = commaR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : Ξ“' = hole ∧ Ο†' = (l✝ ,ᡇ ↑r✝ Ο†) ∨ (βˆƒ Ξ“'_1, Ξ“' = commaL Ξ“'_1 (↑r✝ Ο†) ∧ ↑Γ'_1 Ο†' = l✝) ∨ βˆƒ Ξ“'_1, Ξ“' = commaR l✝ Ξ“'_1 ∧ ↑Γ'_1 Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (commaR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = commaR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = commaR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rw [eq_semi] at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : ↑Γ' Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“' : BunchWithHole P h : Ξ“' = hole ∧ Ο†' = (l✝ ;ᡇ ↑r✝ Ο†) ∨ (βˆƒ Ξ“'_1, Ξ“' = semiL Ξ“'_1 (↑r✝ Ο†) ∧ ↑Γ'_1 Ο†' = l✝) ∨ βˆƒ Ξ“'_1, Ξ“' = semiR l✝ Ξ“'_1 ∧ ↑Γ'_1 Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp
case inl.intro P : Sort u_1 Ο† l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' (l✝ ;ᡇ ↑r✝ Ο†) β†’ (βˆƒ Ξ”, Ο† = ↑Δ (l✝ ;ᡇ ↑r✝ Ο†) ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, (l✝ ;ᡇ ↑r✝ Ο†) = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' (l✝ ;ᡇ ↑r✝ Ο†) = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ (l✝ ;ᡇ ↑r✝ Ο†) ∧ (semiR l✝ r✝).comp Ξ” = hole) ∨ (βˆƒ Ξ”, (l✝ ;ᡇ ↑r✝ Ο†) = ↑Δ Ο† ∧ hole.comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = hole ∧ Ξ”' (l✝ ;ᡇ ↑r✝ Ο†) = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = semiR l✝ Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiR l✝ Ξ“'').comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiR l✝ Ξ“'' ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rw [eq_comm] at h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = ↑r✝ Ο† ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑r✝ Ο† = ↑Γ'' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
rcases ih h with (h1|h2|βŸ¨Ξ”,Ξ”',rfl,rfl,h3⟩) <;> clear ih h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑r✝ Ο† = ↑Γ'' Ο†' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
case inl P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ Ξ“'' : BunchWithHole P h1 : βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ case inr.inl P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ Ξ“'' : BunchWithHole P h2 : βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ case inr.inr.intro.intro.intro.intro P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”_1, Ο† = ↑Δ_1 Ο†' ∧ (Ξ”' Ο†').comp Ξ”_1 = Ξ” Ο†) ∨ (βˆƒ Ξ”_1, Ο†' = ↑Δ_1 Ο† ∧ (Ξ” Ο†).comp Ξ”_1 = Ξ”' Ο†') ∨ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp [h1]
case inl P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ Ξ“'' : BunchWithHole P h1 : βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'' ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp [h2]
case inr.inl P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ Ξ“'' : BunchWithHole P h2 : βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“'') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“''.comp Ξ” = r✝) ∨ βˆƒ Ξ”, Ξ” Ο† = semiR l✝ Ξ“'' ∧ βˆƒ x, x Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
apply Or.inr
case inr.inr.intro.intro.intro.intro P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”_1, Ο† = ↑Δ_1 Ο†' ∧ (Ξ”' Ο†').comp Ξ”_1 = Ξ” Ο†) ∨ (βˆƒ Ξ”_1, Ο†' = ↑Δ_1 Ο† ∧ (Ξ” Ο†).comp Ξ”_1 = Ξ”' Ο†') ∨ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”_1, Ο†' = ↑Δ_1 Ο† ∧ (Ξ” Ο†).comp Ξ”_1 = Ξ”' Ο†') ∨ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
apply Or.inr
case inr.inr.intro.intro.intro.intro.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ (βˆƒ Ξ”_1, Ο†' = ↑Δ_1 Ο† ∧ (Ξ” Ο†).comp Ξ”_1 = Ξ”' Ο†') ∨ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
iterate 2 ( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ Ξ”_1, Ξ”_1 Ο† = semiR l✝ (Ξ” Ο†) ∧ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ”_1 ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
intro ψ ψ'
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ψ ψ' : Bunch P ⊒ ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp [h3]
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ψ ψ' : Bunch P ⊒ ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => commaL _ _),rfl,?_⟩
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' r✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = commaL (Ξ”' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaL (Ξ” x) r✝) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' r✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaL (Ξ” x) r✝) ψ) ψ' = ↑((fun x => commaL (Ξ”' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => commaR _ _),rfl,?_⟩
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = commaR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Ξ” x)) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => commaR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => semiL _ _),rfl,?_⟩
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' r✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = semiL (Ξ”' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL (Ξ” x) r✝) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' r✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL (Ξ” x) r✝) ψ) ψ' = ↑((fun x => semiL (Ξ”' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => semiR _ _),rfl,?_⟩
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆƒ x, x Ο†' = semiR l✝ (Ξ”' Ο†') ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 Ο† Ο†' l✝ : Bunch P Ξ” Ξ”' : Bunch P β†’ BunchWithHole P h3 : βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Ξ” x)) ψ) ψ' = ↑((fun x => semiR l✝ (Ξ”' x)) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
cases h
P : Sort u_1 Ο† Ο†' l✝ : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P h : ↑Γ'' Ο†' = l✝ ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR l✝ r✝).comp Ξ” = semiL Ξ“'' (↑r✝ Ο†)) ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiL Ξ“'' (↑r✝ Ο†)).comp Ξ” = semiR l✝ r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ Ξ”' Ο†' = semiR l✝ r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR (↑Γ'' Ο†') r✝).comp Ξ” = semiL Ξ“'' (↑r✝ Ο†)) ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiL Ξ“'' (↑r✝ Ο†)).comp Ξ” = semiR (↑Γ'' Ο†') r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ Ξ”' Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ (semiR (↑Γ'' Ο†') r✝).comp Ξ” = semiL Ξ“'' (↑r✝ Ο†)) ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ (semiL Ξ“'' (↑r✝ Ο†)).comp Ξ” = semiR (↑Γ'' Ο†') r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ Ξ”' Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ Ξ”, Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
iterate 2 ( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ Ξ”, Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
intro ψ ψ'
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ψ ψ' : Bunch P ⊒ ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
simp
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ψ ψ' : Bunch P ⊒ ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => commaL _ _),rfl,?_⟩
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ Ξ”, Ξ” Ο† = commaL Ξ“'' (↑r✝ Ο†) ∧ βˆƒ x, x Ο†' = commaR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = commaR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => commaR _ _),rfl,?_⟩
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = commaR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => commaL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => commaR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => semiL _ _),rfl,?_⟩
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ Ξ”, Ξ” Ο† = semiL Ξ“'' (↑r✝ Ο†) ∧ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.eq_inv
[198, 1]
[239, 13]
refine ⟨(fun x => semiR _ _),rfl,?_⟩
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆƒ x, x Ο†' = semiR (↑Γ'' Ο†') r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
case refl P : Sort u_1 Ο† Ο†' : Bunch P r✝ : BunchWithHole P ih : βˆ€ {Ξ“' : BunchWithHole P}, ↑r✝ Ο† = ↑Γ' Ο†' β†’ (βˆƒ Ξ”, Ο† = ↑Δ Ο†' ∧ r✝.comp Ξ” = Ξ“') ∨ (βˆƒ Ξ”, Ο†' = ↑Δ Ο† ∧ Ξ“'.comp Ξ” = r✝) ∨ βˆƒ Ξ” Ξ”', Ξ” Ο† = Ξ“' ∧ Ξ”' Ο†' = r✝ ∧ βˆ€ (ψ ψ' : Bunch P), ↑(Ξ” ψ) ψ' = ↑(Ξ”' ψ') ψ Ξ“'' : BunchWithHole P ⊒ βˆ€ (ψ ψ' : Bunch P), ↑((fun x => semiL Ξ“'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.idem
[241, 9]
[243, 21]
simp [FunLike.coe]
P : Sort u_1 Ξ“ : BunchWithHole P b : Bunch P ⊒ ↑Γ b = b ↔ Ξ“ = hole
no goals
https://github.com/JamesGallicchio/brunched-invitations.git
3082c5ae68d2022b1439310f315a0038dae24e0c
BunchImpl/Bunch.lean
BunchImpl.BunchWithHole.idem'
[245, 9]
[247, 21]
simp [FunLike.coe]
P : Sort u_1 Ξ“ : BunchWithHole P b : Bunch P ⊒ b = ↑Γ b ↔ Ξ“ = hole
no goals