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stringclasses 147
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stringclasses 147
values | file_path
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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
| input
stringlengths 73
2.09M
|
|---|---|---|---|---|---|---|---|---|---|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
intros a b c
|
β’ β (a b c : Rotation), a + b + c = a + (b + c)
|
a b c : Rotation
β’ a + b + c = a + (b + c)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a b c : Rotation), a + b + c = a + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
cases a
|
a b c : Rotation
β’ a + b + c = a + (b + c)
|
case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
|
Please generate a tactic in lean4 to solve the state.
STATE:
a b c : Rotation
β’ a + b + c = a + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
repeat {
cases b
repeat {
cases c
repeat { rfl }
}
}
|
case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
b c : Rotation
β’ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
β’ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
cases b
|
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
|
case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240
b c : Rotation
β’ r240 + b + c = r240 + (b + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
repeat {
cases c
repeat { rfl }
}
|
case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r0
c : Rotation
β’ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
β’ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
cases c
|
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
|
case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240
c : Rotation
β’ r240 + r240 + c = r240 + (r240 + c)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
repeat { rfl }
|
case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240.r0
β’ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
β’ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_assoc
|
[134, 1]
|
[144, 4]
|
rfl
|
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240.r240.r240
β’ r240 + r240 + r240 = r240 + (r240 + r240)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_add
|
[157, 1]
|
[161, 17]
|
intro a
|
β’ β (a : Rotation), 0 + a = a
|
a : Rotation
β’ 0 + a = a
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), 0 + a = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_add
|
[157, 1]
|
[161, 17]
|
cases a
|
a : Rotation
β’ 0 + a = a
|
case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240
|
Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ 0 + a = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_add
|
[157, 1]
|
[161, 17]
|
repeat { rfl }
|
case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ 0 + r0 = r0
case r120
β’ 0 + r120 = r120
case r240
β’ 0 + r240 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_add
|
[157, 1]
|
[161, 17]
|
rfl
|
case r240
β’ 0 + r240 = r240
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ 0 + r240 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_zero
|
[163, 1]
|
[167, 17]
|
intro a
|
β’ β (a : Rotation), a + 0 = a
|
a : Rotation
β’ a + 0 = a
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), a + 0 = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_zero
|
[163, 1]
|
[167, 17]
|
cases a
|
a : Rotation
β’ a + 0 = a
|
case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240
|
Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ a + 0 = a
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_zero
|
[163, 1]
|
[167, 17]
|
repeat { rfl }
|
case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ r0 + 0 = r0
case r120
β’ r120 + 0 = r120
case r240
β’ r240 + 0 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_zero
|
[163, 1]
|
[167, 17]
|
rfl
|
case r240
β’ r240 + 0 = r240
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ r240 + 0 = r240
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_vadd
|
[219, 1]
|
[223, 17]
|
intro p
|
β’ β (p : State), 0 +α΅₯ p = p
|
p : State
β’ 0 +α΅₯ p = p
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (p : State), 0 +α΅₯ p = p
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_vadd
|
[219, 1]
|
[223, 17]
|
cases p
|
p : State
β’ 0 +α΅₯ p = p
|
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
|
Please generate a tactic in lean4 to solve the state.
STATE:
p : State
β’ 0 +α΅₯ p = p
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_vadd
|
[219, 1]
|
[223, 17]
|
repeat { rfl }
|
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_zero_vadd
|
[219, 1]
|
[223, 17]
|
rfl
|
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case heading
hβ : K
unitβ : β
β’ 0 +α΅₯ heading hβ unitβ = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
intros gβ gβ p
|
β’ β (gβ gβ : Rotation) (p : State), gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
|
gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (gβ gβ : Rotation) (p : State), gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
cases gβ
|
gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
|
case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p)
|
Please generate a tactic in lean4 to solve the state.
STATE:
gβ gβ : Rotation
p : State
β’ gβ + gβ +α΅₯ p = gβ +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
repeat {
cases gβ
repeat {
cases p
repeat rfl
}
}
|
case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p)
|
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
gβ : Rotation
p : State
β’ r0 + gβ +α΅₯ p = r0 +α΅₯ (gβ +α΅₯ p)
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
case r240
gβ : Rotation
p : State
β’ r240 + gβ +α΅₯ p = r240 +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
cases gβ
|
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
|
case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r120
gβ : Rotation
p : State
β’ r120 + gβ +α΅₯ p = r120 +α΅₯ (gβ +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
repeat {
cases p
repeat rfl
}
|
case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
|
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r0
p : State
β’ r120 + r0 +α΅₯ p = r120 +α΅₯ (r0 +α΅₯ p)
case r120.r120
p : State
β’ r120 + r120 +α΅₯ p = r120 +α΅₯ (r120 +α΅₯ p)
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
cases p
|
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
|
case r120.r240.heading
hβ : K
unitβ : β
β’ r120 + r240 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r240 +α΅₯ heading hβ unitβ)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r240
p : State
β’ r120 + r240 +α΅₯ p = r120 +α΅₯ (r240 +α΅₯ p)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
repeat rfl
|
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_vadd
|
[225, 1]
|
[235, 4]
|
rfl
|
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r120.r120.heading
hβ : K
unitβ : β
β’ r120 + r120 +α΅₯ heading hβ unitβ = r120 +α΅₯ (r120 +α΅₯ heading hβ unitβ)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_neg_left
|
[349, 1]
|
[353, 17]
|
intro a
|
β’ β (a : Rotation), -a + a = 0
|
a : Rotation
β’ -a + a = 0
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (a : Rotation), -a + a = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_neg_left
|
[349, 1]
|
[353, 17]
|
cases a
|
a : Rotation
β’ -a + a = 0
|
case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0
|
Please generate a tactic in lean4 to solve the state.
STATE:
a : Rotation
β’ -a + a = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_neg_left
|
[349, 1]
|
[353, 17]
|
repeat { rfl }
|
case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
β’ -r0 + r0 = 0
case r120
β’ -r120 + r120 = 0
case r240
β’ -r240 + r240 = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_add_neg_left
|
[349, 1]
|
[353, 17]
|
rfl
|
case r240
β’ -r240 + r240 = 0
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r240
β’ -r240 + r240 = 0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vsub_vadd'
|
[405, 1]
|
[412, 4]
|
intro p1 p2
|
β’ β (p1 p2 : State), p1 -α΅₯ p2 +α΅₯ p2 = p1
|
p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (p1 p2 : State), p1 -α΅₯ p2 +α΅₯ p2 = p1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vsub_vadd'
|
[405, 1]
|
[412, 4]
|
cases p1
|
p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1
|
case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ
|
Please generate a tactic in lean4 to solve the state.
STATE:
p1 p2 : State
β’ p1 -α΅₯ p2 +α΅₯ p2 = p1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vsub_vadd'
|
[405, 1]
|
[412, 4]
|
cases p2
|
case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ
|
case heading.heading
hβΒΉ : K
unitβΒΉ : β
hβ : K
unitβ : β
β’ heading hβΒΉ unitβΒΉ -α΅₯ heading hβ unitβ +α΅₯ heading hβ unitβ = heading hβΒΉ unitβΒΉ
|
Please generate a tactic in lean4 to solve the state.
STATE:
case heading
p2 : State
hβ : K
unitβ : β
β’ heading hβ unitβ -α΅₯ p2 +α΅₯ p2 = heading hβ unitβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vadd_vsub'
|
[414, 1]
|
[421, 4]
|
intros g p
|
β’ β (g : Rotation) (p : State), g +α΅₯ p -α΅₯ p = g
|
g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (g : Rotation) (p : State), g +α΅₯ p -α΅₯ p = g
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vadd_vsub'
|
[414, 1]
|
[421, 4]
|
cases g
|
g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g
|
case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0
case r120
p : State
β’ r120 +α΅₯ p -α΅₯ p = r120
case r240
p : State
β’ r240 +α΅₯ p -α΅₯ p = r240
|
Please generate a tactic in lean4 to solve the state.
STATE:
g : Rotation
p : State
β’ g +α΅₯ p -α΅₯ p = g
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/vector_spaces.lean
|
rot_state_vadd_vsub'
|
[414, 1]
|
[421, 4]
|
cases p
|
case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0
|
case r0.heading
hβ : K
unitβ : β
β’ r0 +α΅₯ heading hβ unitβ -α΅₯ heading hβ unitβ = r0
|
Please generate a tactic in lean4 to solve the state.
STATE:
case r0
p : State
β’ r0 +α΅₯ p -α΅₯ p = r0
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_refl
|
[68, 1]
|
[71, 12]
|
unfold Reflexive
|
β’ Reflexive Eq
|
β’ β (x : β), x = x
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Reflexive Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_refl
|
[68, 1]
|
[71, 12]
|
intro x
|
β’ β (x : β), x = x
|
x : β
β’ x = x
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (x : β), x = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_refl
|
[68, 1]
|
[71, 12]
|
exact rfl
|
x : β
β’ x = x
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
x : β
β’ x = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_symm
|
[73, 1]
|
[77, 11]
|
unfold Symmetric
|
β’ Symmetric Eq
|
β’ β β¦x y : ββ¦, x = y β y = x
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Symmetric Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_symm
|
[73, 1]
|
[77, 11]
|
intro x y
|
β’ β β¦x y : ββ¦, x = y β y = x
|
x y : β
β’ x = y β y = x
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦x y : ββ¦, x = y β y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_symm
|
[73, 1]
|
[77, 11]
|
intro hxy
|
x y : β
β’ x = y β y = x
|
x y : β
hxy : x = y
β’ y = x
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y : β
β’ x = y β y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_symm
|
[73, 1]
|
[77, 11]
|
rw [hxy]
|
x y : β
hxy : x = y
β’ y = x
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y : β
hxy : x = y
β’ y = x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_trans
|
[82, 1]
|
[87, 9]
|
unfold Transitive
|
β’ Transitive Eq
|
β’ β β¦x y z : ββ¦, x = y β y = z β x = z
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Transitive Eq
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_trans
|
[82, 1]
|
[87, 9]
|
intros x y z
|
β’ β β¦x y z : ββ¦, x = y β y = z β x = z
|
x y z : β
β’ x = y β y = z β x = z
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦x y z : ββ¦, x = y β y = z β x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_trans
|
[82, 1]
|
[87, 9]
|
intros hxy hyz
|
x y z : β
β’ x = y β y = z β x = z
|
x y z : β
hxy : x = y
hyz : y = z
β’ x = z
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
β’ x = y β y = z β x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_trans
|
[82, 1]
|
[87, 9]
|
rw [hxy]
|
x y z : β
hxy : x = y
hyz : y = z
β’ x = z
|
x y z : β
hxy : x = y
hyz : y = z
β’ y = z
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
hxy : x = y
hyz : y = z
β’ x = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
eq_nat_is_trans
|
[82, 1]
|
[87, 9]
|
rw [hyz]
|
x y z : β
hxy : x = y
hyz : y = z
β’ y = z
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y z : β
hxy : x = y
hyz : y = z
β’ y = z
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv'
|
[99, 1]
|
[102, 31]
|
intro n
|
β’ β (n : β), Equivalence (cong_mod_n n)
|
n : β
β’ Equivalence (cong_mod_n n)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_rfl
|
[106, 1]
|
[111, 12]
|
intro n
|
β’ β (n : β), Reflexive (cong_mod_n n)
|
n : β
β’ Reflexive (cong_mod_n n)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Reflexive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_rfl
|
[106, 1]
|
[111, 12]
|
unfold cong_mod_n
|
n : β
β’ Reflexive (cong_mod_n n)
|
n : β
β’ Reflexive fun a b => a % n = b % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Reflexive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_rfl
|
[106, 1]
|
[111, 12]
|
unfold Reflexive
|
n : β
β’ Reflexive fun a b => a % n = b % n
|
n : β
β’ β (x : β), (fun a b => a % n = b % n) x x
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Reflexive fun a b => a % n = b % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_rfl
|
[106, 1]
|
[111, 12]
|
intro a
|
n : β
β’ β (x : β), (fun a b => a % n = b % n) x x
|
n a : β
β’ a % n = a % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β (x : β), (fun a b => a % n = b % n) x x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_rfl
|
[106, 1]
|
[111, 12]
|
exact rfl
|
n a : β
β’ a % n = a % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n a : β
β’ a % n = a % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
intro n
|
β’ β (n : β), Symmetric (cong_mod_n n)
|
n : β
β’ Symmetric (cong_mod_n n)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Symmetric (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
unfold Symmetric
|
n : β
β’ Symmetric (cong_mod_n n)
|
n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Symmetric (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
intros x y
|
n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x
|
n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β β¦x y : ββ¦, cong_mod_n n x y β cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
intro hxy
|
n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x
|
n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
β’ cong_mod_n n x y β cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
unfold cong_mod_n
|
n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x
|
n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : cong_mod_n n x y
β’ cong_mod_n n y x
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
unfold cong_mod_n at hxy
|
n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n
|
n x y : β
hxy : x % n = y % n
β’ y % n = x % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : cong_mod_n n x y
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_symm
|
[113, 1]
|
[120, 11]
|
rw [hxy]
|
n x y : β
hxy : x % n = y % n
β’ y % n = x % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
hxy : x % n = y % n
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_trans
|
[122, 1]
|
[126, 16]
|
intro n a b c hab hbc
|
β’ β (n : β), Transitive (cong_mod_n n)
|
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Transitive (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_trans
|
[122, 1]
|
[126, 16]
|
unfold cong_mod_n
|
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c
|
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ cong_mod_n n a c
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_trans
|
[122, 1]
|
[126, 16]
|
unfold cong_mod_n at hab hbc
|
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n
|
n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : cong_mod_n n a b
hbc : cong_mod_n n b c
β’ a % n = c % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_trans
|
[122, 1]
|
[126, 16]
|
rw [hab, hbc]
|
n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n a b c : β
hab : a % n = b % n
hbc : b % n = c % n
β’ a % n = c % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
intro n
|
β’ β (n : β), Equivalence (cong_mod_n n)
|
n : β
β’ Equivalence (cong_mod_n n)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (n : β), Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
unfold cong_mod_n
|
n : β
β’ Equivalence (cong_mod_n n)
|
n : β
β’ Equivalence fun a b => a % n = b % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Equivalence (cong_mod_n n)
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
exact Equivalence.mk
(by intro x; rfl)
(by intros x y h; rw [h])
(by intros x y z hxy hyz; rw [hxy, hyz])
|
n : β
β’ Equivalence fun a b => a % n = b % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ Equivalence fun a b => a % n = b % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
intro x
|
n : β
β’ β (x : β), x % n = x % n
|
n x : β
β’ x % n = x % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β (x : β), x % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
rfl
|
n x : β
β’ x % n = x % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x : β
β’ x % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
intros x y h
|
n : β
β’ β {x y : β}, x % n = y % n β y % n = x % n
|
n x y : β
h : x % n = y % n
β’ y % n = x % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β {x y : β}, x % n = y % n β y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
rw [h]
|
n x y : β
h : x % n = y % n
β’ y % n = x % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y : β
h : x % n = y % n
β’ y % n = x % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
intros x y z hxy hyz
|
n : β
β’ β {x y z : β}, x % n = y % n β y % n = z % n β x % n = z % n
|
n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n
|
Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β {x y z : β}, x % n = y % n β y % n = z % n β x % n = z % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
cong_mod_n_equiv
|
[128, 1]
|
[135, 47]
|
rw [hxy, hyz]
|
n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
n x y z : β
hxy : x % n = y % n
hyz : y % n = z % n
β’ x % n = z % n
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
succ_inj
|
[189, 1]
|
[193, 13]
|
unfold Injective
|
β’ Injective fun n => n + 1
|
β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective fun n => n + 1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
succ_inj
|
[189, 1]
|
[193, 13]
|
intros a1 a2 h
|
β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ
|
a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦aβ aβ : ββ¦, (fun n => n + 1) aβ = (fun n => n + 1) aβ β aβ = aβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
succ_inj
|
[189, 1]
|
[193, 13]
|
simp [Nat.add] at h
|
a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2
|
a1 a2 : β
h : a1 = a2
β’ a1 = a2
|
Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : β
h : (fun n => n + 1) a1 = (fun n => n + 1) a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
succ_inj
|
[189, 1]
|
[193, 13]
|
assumption
|
a1 a2 : β
h : a1 = a2
β’ a1 = a2
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : β
h : a1 = a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_succ_surj
|
[196, 1]
|
[200, 27]
|
unfold Surjective
|
β’ Β¬Surjective fun n => n + 1
|
β’ Β¬β (b : β), β a, (fun n => n + 1) a = b
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Β¬Surjective fun n => n + 1
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_succ_surj
|
[196, 1]
|
[200, 27]
|
intro h
|
β’ Β¬β (b : β), β a, (fun n => n + 1) a = b
|
h : β (b : β), β a, (fun n => n + 1) a = b
β’ False
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Β¬β (b : β), β a, (fun n => n + 1) a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_succ_surj
|
[196, 1]
|
[200, 27]
|
let contra := h 0
|
h : β (b : β), β a, (fun n => n + 1) a = b
β’ False
|
h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False
|
Please generate a tactic in lean4 to solve the state.
STATE:
h : β (b : β), β a, (fun n => n + 1) a = b
β’ False
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_succ_surj
|
[196, 1]
|
[200, 27]
|
simp [Nat.add] at contra
|
h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
h : β (b : β), β a, (fun n => n + 1) a = b
contra : β a, (fun n => n + 1) a = 0 := h 0
β’ False
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
unfold Injective
|
β’ Injective Bool.not
|
β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
intros a1 a2 h
|
β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ
|
a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β β¦aβ aβ : Boolβ¦, Bool.not aβ = Bool.not aβ β aβ = aβ
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
cases a1 with
| true =>
cases a2 with
| true => rfl
| false => nomatch h
| false =>
cases a2 with
| true => nomatch h
| false => rfl
|
a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
a1 a2 : Bool
h : Bool.not a1 = Bool.not a2
β’ a1 = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
cases a2 with
| true => rfl
| false => nomatch h
|
case true
a2 : Bool
h : Bool.not true = Bool.not a2
β’ true = a2
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case true
a2 : Bool
h : Bool.not true = Bool.not a2
β’ true = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
rfl
|
case true.true
h : Bool.not true = Bool.not true
β’ true = true
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case true.true
h : Bool.not true = Bool.not true
β’ true = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
nomatch h
|
case true.false
h : Bool.not true = Bool.not false
β’ true = false
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case true.false
h : Bool.not true = Bool.not false
β’ true = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
cases a2 with
| true => nomatch h
| false => rfl
|
case false
a2 : Bool
h : Bool.not false = Bool.not a2
β’ false = a2
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case false
a2 : Bool
h : Bool.not false = Bool.not a2
β’ false = a2
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
nomatch h
|
case false.true
h : Bool.not false = Bool.not true
β’ false = true
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case false.true
h : Bool.not false = Bool.not true
β’ false = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
inj_not
|
[204, 1]
|
[215, 25]
|
rfl
|
case false.false
h : Bool.not false = Bool.not false
β’ false = false
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case false.false
h : Bool.not false = Bool.not false
β’ false = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
surj_not
|
[217, 1]
|
[222, 33]
|
unfold Surjective
|
β’ Surjective Bool.not
|
β’ β (b : Bool), β a, Bool.not a = b
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Surjective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
surj_not
|
[217, 1]
|
[222, 33]
|
intro b
|
β’ β (b : Bool), β a, Bool.not a = b
|
b : Bool
β’ β a, Bool.not a = b
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (b : Bool), β a, Bool.not a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
surj_not
|
[217, 1]
|
[222, 33]
|
cases b with
| true => exact β¨ false, rfl β©
| false => exact β¨ true, rfl β©
|
b : Bool
β’ β a, Bool.not a = b
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
β’ β a, Bool.not a = b
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
surj_not
|
[217, 1]
|
[222, 33]
|
exact β¨ false, rfl β©
|
case true
β’ β a, Bool.not a = true
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case true
β’ β a, Bool.not a = true
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
surj_not
|
[217, 1]
|
[222, 33]
|
exact β¨ true, rfl β©
|
case false
β’ β a, Bool.not a = false
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case false
β’ β a, Bool.not a = false
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_bij
|
[224, 1]
|
[226, 30]
|
unfold Bijective
|
β’ Bijective Bool.not
|
β’ Injective Bool.not β§ Surjective Bool.not
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ Bijective Bool.not
TACTIC:
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/sets_relations.lean
|
not_bij
|
[224, 1]
|
[226, 30]
|
exact β¨ inj_not, surj_not β©
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β’ Injective Bool.not β§ Surjective Bool.not
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no goals
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Please generate a tactic in lean4 to solve the state.
STATE:
β’ Injective Bool.not β§ Surjective Bool.not
TACTIC:
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