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/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
intros a b c
|
⊢ ∀ (a b c : Rotation), a + b + c = a + (b + c)
|
a b c : Rotation
⊢ a + b + c = a + (b + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
cases a
|
a b c : Rotation
⊢ a + b + c = a + (b + c)
|
case r0
b c : Rotation
⊢ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
⊢ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
repeat {
cases b
repeat {
cases c
repeat { rfl }
}
}
|
case r0
b c : Rotation
⊢ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
⊢ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
cases b
|
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
case r240.r0
c : Rotation
⊢ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
⊢ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
repeat {
cases c
repeat { rfl }
}
|
case r240.r0
c : Rotation
⊢ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
⊢ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
cases c
|
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
case r240.r240.r0
⊢ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
⊢ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
repeat { rfl }
|
case r240.r240.r0
⊢ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
⊢ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_assoc
|
[140, 1]
|
[150, 4]
|
rfl
|
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_add
|
[163, 1]
|
[167, 17]
|
intro a
|
⊢ ∀ (a : Rotation), 0 + a = a
|
a : Rotation
⊢ 0 + a = a
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_add
|
[163, 1]
|
[167, 17]
|
cases a
|
a : Rotation
⊢ 0 + a = a
|
case r0
⊢ 0 + r0 = r0
case r120
⊢ 0 + r120 = r120
case r240
⊢ 0 + r240 = r240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_add
|
[163, 1]
|
[167, 17]
|
repeat { rfl }
|
case r0
⊢ 0 + r0 = r0
case r120
⊢ 0 + r120 = r120
case r240
⊢ 0 + r240 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_add
|
[163, 1]
|
[167, 17]
|
rfl
|
case r240
⊢ 0 + r240 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_zero
|
[169, 1]
|
[173, 17]
|
intro a
|
⊢ ∀ (a : Rotation), a + 0 = a
|
a : Rotation
⊢ a + 0 = a
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_zero
|
[169, 1]
|
[173, 17]
|
cases a
|
a : Rotation
⊢ a + 0 = a
|
case r0
⊢ r0 + 0 = r0
case r120
⊢ r120 + 0 = r120
case r240
⊢ r240 + 0 = r240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_zero
|
[169, 1]
|
[173, 17]
|
repeat { rfl }
|
case r0
⊢ r0 + 0 = r0
case r120
⊢ r120 + 0 = r120
case r240
⊢ r240 + 0 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_zero
|
[169, 1]
|
[173, 17]
|
rfl
|
case r240
⊢ r240 + 0 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_vadd
|
[225, 1]
|
[229, 17]
|
intro p
|
⊢ ∀ (p : State), 0 +ᵥ p = p
|
p : State
⊢ 0 +ᵥ p = p
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_vadd
|
[225, 1]
|
[229, 17]
|
cases p
|
p : State
⊢ 0 +ᵥ p = p
|
case s0
⊢ 0 +ᵥ s0 = s0
case s120
⊢ 0 +ᵥ s120 = s120
case s240
⊢ 0 +ᵥ s240 = s240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_vadd
|
[225, 1]
|
[229, 17]
|
repeat { rfl }
|
case s0
⊢ 0 +ᵥ s0 = s0
case s120
⊢ 0 +ᵥ s120 = s120
case s240
⊢ 0 +ᵥ s240 = s240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_zero_vadd
|
[225, 1]
|
[229, 17]
|
rfl
|
case s240
⊢ 0 +ᵥ s240 = s240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
intros g₁ g₂ p
|
⊢ ∀ (g₁ g₂ : Rotation) (p : State), g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)
|
g₁ g₂ : Rotation
p : State
⊢ g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
cases g₁
|
g₁ g₂ : Rotation
p : State
⊢ g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)
|
case r0
g₂ : Rotation
p : State
⊢ r0 + g₂ +ᵥ p = r0 +ᵥ (g₂ +ᵥ p)
case r120
g₂ : Rotation
p : State
⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p)
case r240
g₂ : Rotation
p : State
⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
repeat {
cases g₂
repeat {
cases p
repeat rfl
}
}
|
case r0
g₂ : Rotation
p : State
⊢ r0 + g₂ +ᵥ p = r0 +ᵥ (g₂ +ᵥ p)
case r120
g₂ : Rotation
p : State
⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p)
case r240
g₂ : Rotation
p : State
⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
cases g₂
|
case r240
g₂ : Rotation
p : State
⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)
|
case r240.r0
p : State
⊢ r240 + r0 +ᵥ p = r240 +ᵥ (r0 +ᵥ p)
case r240.r120
p : State
⊢ r240 + r120 +ᵥ p = r240 +ᵥ (r120 +ᵥ p)
case r240.r240
p : State
⊢ r240 + r240 +ᵥ p = r240 +ᵥ (r240 +ᵥ p)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
repeat {
cases p
repeat rfl
}
|
case r240.r0
p : State
⊢ r240 + r0 +ᵥ p = r240 +ᵥ (r0 +ᵥ p)
case r240.r120
p : State
⊢ r240 + r120 +ᵥ p = r240 +ᵥ (r120 +ᵥ p)
case r240.r240
p : State
⊢ r240 + r240 +ᵥ p = r240 +ᵥ (r240 +ᵥ p)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
cases p
|
case r240.r240
p : State
⊢ r240 + r240 +ᵥ p = r240 +ᵥ (r240 +ᵥ p)
|
case r240.r240.s0
⊢ r240 + r240 +ᵥ s0 = r240 +ᵥ (r240 +ᵥ s0)
case r240.r240.s120
⊢ r240 + r240 +ᵥ s120 = r240 +ᵥ (r240 +ᵥ s120)
case r240.r240.s240
⊢ r240 + r240 +ᵥ s240 = r240 +ᵥ (r240 +ᵥ s240)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
repeat rfl
|
case r240.r240.s0
⊢ r240 + r240 +ᵥ s0 = r240 +ᵥ (r240 +ᵥ s0)
case r240.r240.s120
⊢ r240 + r240 +ᵥ s120 = r240 +ᵥ (r240 +ᵥ s120)
case r240.r240.s240
⊢ r240 + r240 +ᵥ s240 = r240 +ᵥ (r240 +ᵥ s240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_vadd
|
[231, 1]
|
[241, 4]
|
rfl
|
case r240.r240.s240
⊢ r240 + r240 +ᵥ s240 = r240 +ᵥ (r240 +ᵥ s240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_neg_left
|
[355, 1]
|
[359, 17]
|
intro a
|
⊢ ∀ (a : Rotation), -a + a = 0
|
a : Rotation
⊢ -a + a = 0
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_neg_left
|
[355, 1]
|
[359, 17]
|
cases a
|
a : Rotation
⊢ -a + a = 0
|
case r0
⊢ -r0 + r0 = 0
case r120
⊢ -r120 + r120 = 0
case r240
⊢ -r240 + r240 = 0
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_neg_left
|
[355, 1]
|
[359, 17]
|
repeat { rfl }
|
case r0
⊢ -r0 + r0 = 0
case r120
⊢ -r120 + r120 = 0
case r240
⊢ -r240 + r240 = 0
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_add_neg_left
|
[355, 1]
|
[359, 17]
|
rfl
|
case r240
⊢ -r240 + r240 = 0
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
intro p1 p2
|
⊢ ∀ (p1 p2 : State), p1 -ᵥ p2 +ᵥ p2 = p1
|
p1 p2 : State
⊢ p1 -ᵥ p2 +ᵥ p2 = p1
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
cases p1
|
p1 p2 : State
⊢ p1 -ᵥ p2 +ᵥ p2 = p1
|
case s0
p2 : State
⊢ s0 -ᵥ p2 +ᵥ p2 = s0
case s120
p2 : State
⊢ s120 -ᵥ p2 +ᵥ p2 = s120
case s240
p2 : State
⊢ s240 -ᵥ p2 +ᵥ p2 = s240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
repeat {
cases p2
repeat rfl
}
|
case s0
p2 : State
⊢ s0 -ᵥ p2 +ᵥ p2 = s0
case s120
p2 : State
⊢ s120 -ᵥ p2 +ᵥ p2 = s120
case s240
p2 : State
⊢ s240 -ᵥ p2 +ᵥ p2 = s240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
cases p2
|
case s240
p2 : State
⊢ s240 -ᵥ p2 +ᵥ p2 = s240
|
case s240.s0
⊢ s240 -ᵥ s0 +ᵥ s0 = s240
case s240.s120
⊢ s240 -ᵥ s120 +ᵥ s120 = s240
case s240.s240
⊢ s240 -ᵥ s240 +ᵥ s240 = s240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
repeat rfl
|
case s240.s0
⊢ s240 -ᵥ s0 +ᵥ s0 = s240
case s240.s120
⊢ s240 -ᵥ s120 +ᵥ s120 = s240
case s240.s240
⊢ s240 -ᵥ s240 +ᵥ s240 = s240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vsub_vadd'
|
[411, 1]
|
[418, 4]
|
rfl
|
case s240.s240
⊢ s240 -ᵥ s240 +ᵥ s240 = s240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
intros g p
|
⊢ ∀ (g : Rotation) (p : State), g +ᵥ p -ᵥ p = g
|
g : Rotation
p : State
⊢ g +ᵥ p -ᵥ p = g
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
cases g
|
g : Rotation
p : State
⊢ g +ᵥ p -ᵥ p = g
|
case r0
p : State
⊢ r0 +ᵥ p -ᵥ p = r0
case r120
p : State
⊢ r120 +ᵥ p -ᵥ p = r120
case r240
p : State
⊢ r240 +ᵥ p -ᵥ p = r240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
repeat {
cases p
repeat { rfl }
}
|
case r0
p : State
⊢ r0 +ᵥ p -ᵥ p = r0
case r120
p : State
⊢ r120 +ᵥ p -ᵥ p = r120
case r240
p : State
⊢ r240 +ᵥ p -ᵥ p = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
cases p
|
case r240
p : State
⊢ r240 +ᵥ p -ᵥ p = r240
|
case r240.s0
⊢ r240 +ᵥ s0 -ᵥ s0 = r240
case r240.s120
⊢ r240 +ᵥ s120 -ᵥ s120 = r240
case r240.s240
⊢ r240 +ᵥ s240 -ᵥ s240 = r240
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
repeat { rfl }
|
case r240.s0
⊢ r240 +ᵥ s0 -ᵥ s0 = r240
case r240.s120
⊢ r240 +ᵥ s120 -ᵥ s120 = r240
case r240.s240
⊢ r240 +ᵥ s240 -ᵥ s240 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries_key.lean
|
rot_state_vadd_vsub'
|
[420, 1]
|
[427, 4]
|
rfl
|
case r240.s240
⊢ r240 +ᵥ s240 -ᵥ s240 = r240
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/16_lecture_more_notes.lean
|
cs2120f23.proof_equal
|
[169, 1]
|
[169, 76]
|
trivial
|
⊢ Birds_chirping.boo = Birds_chirping.yep
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Exams/Final/final_part1_key.lean
|
eq_is_symm
|
[420, 1]
|
[422, 9]
|
rw [h]
|
α : Type
a b : α
h : a = b
⊢ b = a
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Exams/Final/final_part1_key.lean
|
eq_rel_trans
|
[449, 1]
|
[453, 10]
|
rw [ab]
|
α : Type
a b c : α
ab : a = b
bc : b = c
⊢ a = c
|
α : Type
a b c : α
ab : a = b
bc : b = c
⊢ b = c
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Exams/Final/final_part1_key.lean
|
eq_rel_trans
|
[449, 1]
|
[453, 10]
|
rw [bc]
|
α : Type
a b c : α
ab : a = b
bc : b = c
⊢ b = c
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
intros a b c
|
⊢ ∀ (a b c : Rotation), a + b + c = a + (b + c)
|
a b c : Rotation
⊢ a + b + c = a + (b + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
cases a
|
a b c : Rotation
⊢ a + b + c = a + (b + c)
|
case r0
b c : Rotation
⊢ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
⊢ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
repeat {
cases b
repeat {
cases c
repeat { rfl }
}
}
|
case r0
b c : Rotation
⊢ r0 + b + c = r0 + (b + c)
case r120
b c : Rotation
⊢ r120 + b + c = r120 + (b + c)
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
cases b
|
case r240
b c : Rotation
⊢ r240 + b + c = r240 + (b + c)
|
case r240.r0
c : Rotation
⊢ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
⊢ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
repeat {
cases c
repeat { rfl }
}
|
case r240.r0
c : Rotation
⊢ r240 + r0 + c = r240 + (r0 + c)
case r240.r120
c : Rotation
⊢ r240 + r120 + c = r240 + (r120 + c)
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
cases c
|
case r240.r240
c : Rotation
⊢ r240 + r240 + c = r240 + (r240 + c)
|
case r240.r240.r0
⊢ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
⊢ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
repeat { rfl }
|
case r240.r240.r0
⊢ r240 + r240 + r0 = r240 + (r240 + r0)
case r240.r240.r120
⊢ r240 + r240 + r120 = r240 + (r240 + r120)
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_assoc
|
[141, 1]
|
[151, 4]
|
rfl
|
case r240.r240.r240
⊢ r240 + r240 + r240 = r240 + (r240 + r240)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_zero_add
|
[164, 1]
|
[166, 4]
|
_
|
⊢ ∀ (a : Rotation), 0 + a = a
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_zero
|
[168, 1]
|
[170, 4]
|
_
|
⊢ ∀ (a : Rotation), a + 0 = a
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_zero_vadd
|
[222, 1]
|
[224, 4]
|
_
|
⊢ ∀ (p : State), 0 +ᵥ p = p
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_vadd
|
[226, 1]
|
[228, 4]
|
_
|
⊢ ∀ (g₁ g₂ : Rotation) (p : State), g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_add_neg_left
|
[365, 1]
|
[367, 4]
|
_
|
⊢ ∀ (a : Rotation), -a + a = 0
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_state_vsub_vadd'
|
[425, 1]
|
[427, 4]
|
_
|
⊢ ∀ (p1 p2 : State), p1 -ᵥ p2 +ᵥ p2 = p1
|
no goals
|
https://github.com/kevinsullivan/cs2120f23.git
|
c2da7c4a6be769c6fca375a54e8c1fa31ba2854b
|
Instructor/Lectures/grad/case_study_symmetries.lean
|
rot_state_vadd_vsub'
|
[429, 1]
|
[431, 4]
|
_
|
⊢ ∀ (g : Rotation) (p : State), g +ᵥ p -ᵥ p = g
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
induction s
|
α : Type
s : Str α
⊢ ∃ n, List.reverse s ∈ exp α n
|
case nil
α : Type
⊢ ∃ n, [].reverse ∈ exp α n
case cons
α : Type
head✝ : α
tail✝ : List α
tail_ih✝ : ∃ n, tail✝.reverse ∈ exp α n
⊢ ∃ n, (head✝ :: tail✝).reverse ∈ exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
case nil =>
apply Exists.intro 0
exact exp.zero
|
α : Type
⊢ ∃ n, [].reverse ∈ exp α n
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
case cons hd tl ih =>
apply Exists.elim ih
intro n a1
apply Exists.intro (n + 1)
simp
exact exp.succ n hd tl.reverse a1
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
⊢ ∃ n, (hd :: tl).reverse ∈ exp α n
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
apply Exists.intro 0
|
α : Type
⊢ ∃ n, [].reverse ∈ exp α n
|
α : Type
⊢ [].reverse ∈ exp α 0
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
exact exp.zero
|
α : Type
⊢ [].reverse ∈ exp α 0
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
apply Exists.elim ih
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
⊢ ∃ n, (hd :: tl).reverse ∈ exp α n
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
⊢ ∀ (a : ℕ), tl.reverse ∈ exp α a → ∃ n, (hd :: tl).reverse ∈ exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
intro n a1
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
⊢ ∀ (a : ℕ), tl.reverse ∈ exp α a → ∃ n, (hd :: tl).reverse ∈ exp α n
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ ∃ n, (hd :: tl).reverse ∈ exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
apply Exists.intro (n + 1)
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ ∃ n, (hd :: tl).reverse ∈ exp α n
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ (hd :: tl).reverse ∈ exp α (n + 1)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
simp
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ (hd :: tl).reverse ∈ exp α (n + 1)
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ tl.reverse ++ [hd] ∈ exp α (n + 1)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp
|
[53, 1]
|
[67, 40]
|
exact exp.succ n hd tl.reverse a1
|
α : Type
hd : α
tl : List α
ih : ∃ n, tl.reverse ∈ exp α n
n : ℕ
a1 : tl.reverse ∈ exp α n
⊢ tl.reverse ++ [hd] ∈ exp α (n + 1)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp
|
[70, 1]
|
[77, 13]
|
obtain s1 := rev_str_mem_exp s.reverse
|
α : Type
s : Str α
⊢ ∃ n, s ∈ exp α n
|
α : Type
s : Str α
s1 : ∃ n, (List.reverse s).reverse ∈ exp α n
⊢ ∃ n, s ∈ exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp
|
[70, 1]
|
[77, 13]
|
simp only [List.reverse_reverse] at s1
|
α : Type
s : Str α
s1 : ∃ n, (List.reverse s).reverse ∈ exp α n
⊢ ∃ n, s ∈ exp α n
|
α : Type
s : Str α
s1 : ∃ n, s ∈ exp α n
⊢ ∃ n, s ∈ exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp
|
[70, 1]
|
[77, 13]
|
exact s1
|
α : Type
s : Str α
s1 : ∃ n, s ∈ exp α n
⊢ ∃ n, s ∈ exp α n
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
induction s
|
α : Type
s : Str α
⊢ List.reverse s ∈ exp α (List.length s)
|
case nil
α : Type
⊢ [].reverse ∈ exp α [].length
case cons
α : Type
head✝ : α
tail✝ : List α
tail_ih✝ : tail✝.reverse ∈ exp α tail✝.length
⊢ (head✝ :: tail✝).reverse ∈ exp α (head✝ :: tail✝).length
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
case nil =>
simp
exact exp.zero
|
α : Type
⊢ [].reverse ∈ exp α [].length
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
case cons hd tl ih =>
simp
exact exp.succ tl.length hd tl.reverse ih
|
α : Type
hd : α
tl : List α
ih : tl.reverse ∈ exp α tl.length
⊢ (hd :: tl).reverse ∈ exp α (hd :: tl).length
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
simp
|
α : Type
⊢ [].reverse ∈ exp α [].length
|
α : Type
⊢ [] ∈ exp α 0
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
exact exp.zero
|
α : Type
⊢ [] ∈ exp α 0
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
simp
|
α : Type
hd : α
tl : List α
ih : tl.reverse ∈ exp α tl.length
⊢ (hd :: tl).reverse ∈ exp α (hd :: tl).length
|
α : Type
hd : α
tl : List α
ih : tl.reverse ∈ exp α tl.length
⊢ tl.reverse ++ [hd] ∈ exp α (tl.length + 1)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.rev_str_mem_exp_str_len
|
[80, 1]
|
[91, 48]
|
exact exp.succ tl.length hd tl.reverse ih
|
α : Type
hd : α
tl : List α
ih : tl.reverse ∈ exp α tl.length
⊢ tl.reverse ++ [hd] ∈ exp α (tl.length + 1)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp_str_len
|
[94, 1]
|
[101, 13]
|
obtain s1 := rev_str_mem_exp_str_len s.reverse
|
α : Type
s : Str α
⊢ s ∈ exp α (List.length s)
|
α : Type
s : Str α
s1 : (List.reverse s).reverse ∈ exp α (List.reverse s).length
⊢ s ∈ exp α (List.length s)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp_str_len
|
[94, 1]
|
[101, 13]
|
simp at s1
|
α : Type
s : Str α
s1 : (List.reverse s).reverse ∈ exp α (List.reverse s).length
⊢ s ∈ exp α (List.length s)
|
α : Type
s : Str α
s1 : s ∈ exp α (List.length s)
⊢ s ∈ exp α (List.length s)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.str_mem_exp_str_len
|
[94, 1]
|
[101, 13]
|
exact s1
|
α : Type
s : Str α
s1 : s ∈ exp α (List.length s)
⊢ s ∈ exp α (List.length s)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
induction h1
|
α : Type
s : Str α
n : ℕ
h1 : s ∈ exp α n
⊢ List.length s = n
|
case zero
α : Type
s : Str α
n : ℕ
⊢ [].length = 0
case succ
α : Type
s : Str α
n n✝ : ℕ
a✝¹ : α
s✝ : Str α
a✝ : s✝ ∈ exp α n✝
a_ih✝ : List.length s✝ = n✝
⊢ List.length (s✝ ++ [a✝¹]) = n✝ + 1
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
case zero =>
simp
|
α : Type
s : Str α
n : ℕ
⊢ [].length = 0
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
case succ m a s ih_1 ih_2 =>
simp
exact ih_2
|
α : Type
s✝ : Str α
n m : ℕ
a : α
s : Str α
ih_1 : s ∈ exp α m
ih_2 : List.length s = m
⊢ List.length (s ++ [a]) = m + 1
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
simp
|
α : Type
s : Str α
n : ℕ
⊢ [].length = 0
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
simp
|
α : Type
s✝ : Str α
n m : ℕ
a : α
s : Str α
ih_1 : s ∈ exp α m
ih_2 : List.length s = m
⊢ List.length (s ++ [a]) = m + 1
|
α : Type
s✝ : Str α
n m : ℕ
a : α
s : Str α
ih_1 : s ∈ exp α m
ih_2 : List.length s = m
⊢ List.length s = m
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.mem_exp_imp_str_len_eq
|
[104, 1]
|
[116, 17]
|
exact ih_2
|
α : Type
s✝ : Str α
n m : ℕ
a : α
s : Str α
ih_1 : s ∈ exp α m
ih_2 : List.length s = m
⊢ List.length s = m
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.all_str_mem_kleene_closure
|
[153, 1]
|
[160, 24]
|
simp only [kleene_closure]
|
α : Type
s : Str α
⊢ s ∈ kleene_closure α
|
α : Type
s : Str α
⊢ s ∈ ⋃ n, exp α n
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.all_str_mem_kleene_closure
|
[153, 1]
|
[160, 24]
|
simp
|
α : Type
s : Str α
⊢ s ∈ ⋃ n, exp α n
|
α : Type
s : Str α
⊢ ∃ i, s ∈ exp α i
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.all_str_mem_kleene_closure
|
[153, 1]
|
[160, 24]
|
exact str_mem_exp s
|
α : Type
s : Str α
⊢ ∃ i, s ∈ exp α i
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.thm_2
|
[192, 1]
|
[198, 36]
|
symm
|
α : Type
s t u : Str α
⊢ s ++ (t ++ u) = s ++ t ++ u
|
α : Type
s t u : Str α
⊢ s ++ t ++ u = s ++ (t ++ u)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Strings.thm_2
|
[192, 1]
|
[198, 36]
|
exact (List.append_assoc s t u)
|
α : Type
s t u : Str α
⊢ s ++ t ++ u = s ++ (t ++ u)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Languages.thm_3_a
|
[237, 1]
|
[243, 9]
|
simp only [concat]
|
α : Type
L : Language α
⊢ concat L ∅ = ∅
|
α : Type
L : Language α
⊢ {x | ∃ s ∈ L, ∃ t ∈ ∅, s ++ t = x} = ∅
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Languages.thm_3_a
|
[237, 1]
|
[243, 9]
|
simp
|
α : Type
L : Language α
⊢ {x | ∃ s ∈ L, ∃ t ∈ ∅, s ++ t = x} = ∅
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/Parsing/Text.lean
|
Languages.thm_3_b
|
[246, 1]
|
[252, 9]
|
simp only [concat]
|
α : Type
L : Language α
⊢ concat ∅ L = ∅
|
α : Type
L : Language α
⊢ {x | ∃ s ∈ ∅, ∃ t ∈ L, s ++ t = x} = ∅
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.