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/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | pick_goal 6 | case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1)
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1)
case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | . intros n r1 r2
simp_rw [add_mul, AddMonoidAlgebra.single_add, sum_add] | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1)
case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) | case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | pick_goal 7 | case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) | case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1)
case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0 |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | . intros n r1 r2
simp_rw [add_mul, AddMonoidAlgebra.single_add, sum_add] | case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1)
case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0 | case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0 |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | all_goals simp [RingHom.iterate_map_zero, mul_zero, AddMonoidAlgebra.single_zero] | case e_g.h.h.e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
a₃ : ℕ
b₃ : R
⊢ single (a₁ + (a₂ + a₃)) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.e_g.h.h
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ (sum c.toFinsupp fun a₂_1 b₂ => single (a₁ + a₂ + a₂_1) (0 * (↑φ)^[a₁ + a₂] b₂)) = 0
case e_g.h.h.e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), single (a₁ + a) (b₁ * (↑φ)^[a₁] 0) = 0
case e_g.h.h.h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0
case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0 | no goals |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | intros n r1 r2 | case e_g.h.h.e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
⊢ ∀ (a : ℕ) (b₁_1 b₂ : R),
single (a₁ + a) (b₁ * (↑φ)^[a₁] (b₁_1 + b₂)) =
single (a₁ + a) (b₁ * (↑φ)^[a₁] b₁_1) + single (a₁ + a) (b₁ * (↑φ)^[a₁] b₂) | case e_g.h.h.e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
n : ℕ
r1 r2 : R
⊢ single (a₁ + n) (b₁ * (↑φ)^[a₁] (r1 + r2)) = single (a₁ + n) (b₁ * (↑φ)^[a₁] r1) + single (a₁ + n) (b₁ * (↑φ)^[a₁] r2) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | rw [RingHom.iterate_map_add, mul_add, AddMonoidAlgebra.single_add] | case e_g.h.h.e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
a₂ : ℕ
b₂ : R
n : ℕ
r1 r2 : R
⊢ single (a₁ + n) (b₁ * (↑φ)^[a₁] (r1 + r2)) = single (a₁ + n) (b₁ * (↑φ)^[a₁] r1) + single (a₁ + n) (b₁ * (↑φ)^[a₁] r2) | no goals |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | intros n r1 r2 | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ) (b₁_1 b₂ : R),
single (a₁ + a) (b₁ * (↑φ)^[a₁] (b₁_1 + b₂)) =
single (a₁ + a) (b₁ * (↑φ)^[a₁] b₁_1) + single (a₁ + a) (b₁ * (↑φ)^[a₁] b₂) | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
n : ℕ
r1 r2 : R
⊢ single (a₁ + n) (b₁ * (↑φ)^[a₁] (r1 + r2)) = single (a₁ + n) (b₁ * (↑φ)^[a₁] r1) + single (a₁ + n) (b₁ * (↑φ)^[a₁] r2) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | rw [RingHom.iterate_map_add, mul_add, AddMonoidAlgebra.single_add] | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
n : ℕ
r1 r2 : R
⊢ single (a₁ + n) (b₁ * (↑φ)^[a₁] (r1 + r2)) = single (a₁ + n) (b₁ * (↑φ)^[a₁] r1) + single (a₁ + n) (b₁ * (↑φ)^[a₁] r2) | no goals |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | intros n r1 r2 | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
n : ℕ
r1 r2 : R
⊢ (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) ((r1 + r2) * (↑φ)^[n] b₂)) =
(sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r1 * (↑φ)^[n] b₂)) +
sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r2 * (↑φ)^[n] b₂) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | simp_rw [add_mul, AddMonoidAlgebra.single_add, sum_add] | case e_g.h.h.h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
a₁ : ℕ
b₁ : R
n : ℕ
r1 r2 : R
⊢ (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) ((r1 + r2) * (↑φ)^[n] b₂)) =
(sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r1 * (↑φ)^[n] b₂)) +
sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r2 * (↑φ)^[n] b₂) | no goals |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | intros n r1 r2 | case h_add
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ) (b₁ b₂ : R),
(sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) ((b₁ + b₂) * (↑φ)^[a] b₂_1)) =
(sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (b₁ * (↑φ)^[a] b₂)) +
sum c.toFinsupp fun a₂ b₂_1 => single (a + a₂) (b₂ * (↑φ)^[a] b₂_1) | case h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
n : ℕ
r1 r2 : R
⊢ (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) ((r1 + r2) * (↑φ)^[n] b₂)) =
(sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r1 * (↑φ)^[n] b₂)) +
sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r2 * (↑φ)^[n] b₂) |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | simp_rw [add_mul, AddMonoidAlgebra.single_add, sum_add] | case h_add
R : Type u
a✝ b✝ : R
m n✝ : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
n : ℕ
r1 r2 : R
⊢ (sum c.toFinsupp fun a₂ b₂ => single (n + a₂) ((r1 + r2) * (↑φ)^[n] b₂)) =
(sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r1 * (↑φ)^[n] b₂)) +
sum c.toFinsupp fun a₂ b₂ => single (n + a₂) (r2 * (↑φ)^[n] b₂) | no goals |
https://github.com/mariainesdff/skew_polynomials.git | 16371a025f5c867f83ff258a22df5c0341793888 | SkewPolynomials.lean | SkewPolynomial.mul_assoc | [221, 1] | [241, 84] | simp [RingHom.iterate_map_zero, mul_zero, AddMonoidAlgebra.single_zero] | case h_zero
R : Type u
a✝ b✝ : R
m n : ℕ
inst✝ : Semiring R
φ : R →+* R
p q a b c : R[X;φ]
⊢ ∀ (a : ℕ), (sum c.toFinsupp fun a₂ b₂ => single (a + a₂) (0 * (↑φ)^[a] b₂)) = 0 | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw3.lean | HW3.problem_1 | [62, 1] | [63, 8] | sorry | U : Type
A B : Set U
⊢ A ∩ B ∪ A = A | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw3.lean | HW3.problem_2 | [135, 1] | [136, 8] | sorry | U : Type
A B : Set U
⊢ (Aᶜ \ B)ᶜ = A ∪ B | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Library/Defs.lean | BrownCs22.Set.inter_union_cancel_left | [13, 1] | [14, 29] | simp | α : Type u
s t : Set α
⊢ s ∩ t ∪ s = s | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Library/Defs.lean | BrownCs22.Set.inter_union_cancel_right | [16, 1] | [17, 29] | simp | α : Type u
s t : Set α
⊢ s ∩ t ∪ t = t | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | example_1 | [28, 1] | [29, 8] | sorry | p : Prop
⊢ p → p → p | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | example_1' | [41, 1] | [44, 8] | intro hp1 | p : Prop
⊢ p → p → p | p : Prop
hp1 : p
⊢ p → p |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | example_1' | [41, 1] | [44, 8] | intro hp2 | p : Prop
hp1 : p
⊢ p → p | p : Prop
hp1 hp2 : p
⊢ p |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | example_1' | [41, 1] | [44, 8] | sorry | p : Prop
hp1 hp2 : p
⊢ p | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | intro hpqr | p q r s : Prop
⊢ p ∧ q ∧ r → p ∧ r | p q r s : Prop
hpqr : p ∧ q ∧ r
⊢ p ∧ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | eliminate hpqr with hp hqr | p q r s : Prop
hpqr : p ∧ q ∧ r
⊢ p ∧ r | case intro
p q r s : Prop
hp : p
hqr : q ∧ r
⊢ p ∧ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | eliminate hqr with hq hr | case intro
p q r s : Prop
hp : p
hqr : q ∧ r
⊢ p ∧ r | case intro.intro
p q r s : Prop
hp : p
hq : q
hr : r
⊢ p ∧ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | split_goal | case intro.intro
p q r s : Prop
hp : p
hq : q
hr : r
⊢ p ∧ r | case intro.intro.left
p q r s : Prop
hp : p
hq : q
hr : r
⊢ p
case intro.intro.right
p q r s : Prop
hp : p
hq : q
hr : r
⊢ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | { assumption } | case intro.intro.left
p q r s : Prop
hp : p
hq : q
hr : r
⊢ p
case intro.intro.right
p q r s : Prop
hp : p
hq : q
hr : r
⊢ r | case intro.intro.right
p q r s : Prop
hp : p
hq : q
hr : r
⊢ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | { assumption } | case intro.intro.right
p q r s : Prop
hp : p
hq : q
hr : r
⊢ r | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | assumption | case intro.intro.left
p q r s : Prop
hp : p
hq : q
hr : r
⊢ p | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_1 | [71, 1] | [77, 17] | assumption | case intro.intro.right
p q r s : Prop
hp : p
hq : q
hr : r
⊢ r | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_2 | [132, 1] | [138, 16] | intro hpnq | p q r s : Prop
⊢ (p → ¬q) → ¬(p ∧ q) | p q r s : Prop
hpnq : p → ¬q
⊢ ¬(p ∧ q) |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_2 | [132, 1] | [138, 16] | intro hpq | p q r s : Prop
hpnq : p → ¬q
⊢ ¬(p ∧ q) | p q r s : Prop
hpnq : p → ¬q
hpq : p ∧ q
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_2 | [132, 1] | [138, 16] | eliminate hpq with hp hq | p q r s : Prop
hpnq : p → ¬q
hpq : p ∧ q
⊢ False | case intro
p q r s : Prop
hpnq : p → ¬q
hp : p
hq : q
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_2 | [132, 1] | [138, 16] | have hnq : ¬ q := hpnq hp | case intro
p q r s : Prop
hpnq : p → ¬q
hp : p
hq : q
⊢ False | case intro
p q r s : Prop
hpnq : p → ¬q
hp : p
hq : q
hnq : ¬q
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_2 | [132, 1] | [138, 16] | contradiction | case intro
p q r s : Prop
hpnq : p → ¬q
hp : p
hq : q
hnq : ¬q
⊢ False | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | intro h_long_and | p q r s : Prop
⊢ (p ∨ q) ∧ (p → r) ∧ (q → s) → r ∨ s | p q r s : Prop
h_long_and : (p ∨ q) ∧ (p → r) ∧ (q → s)
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | eliminate h_long_and with hpq h_short_and | p q r s : Prop
h_long_and : (p ∨ q) ∧ (p → r) ∧ (q → s)
⊢ r ∨ s | case intro
p q r s : Prop
hpq : p ∨ q
h_short_and : (p → r) ∧ (q → s)
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | eliminate h_short_and with hpr hqs | case intro
p q r s : Prop
hpq : p ∨ q
h_short_and : (p → r) ∧ (q → s)
⊢ r ∨ s | case intro.intro
p q r s : Prop
hpq : p ∨ q
hpr : p → r
hqs : q → s
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | eliminate hpq with hp hq | case intro.intro
p q r s : Prop
hpq : p ∨ q
hpr : p → r
hqs : q → s
⊢ r ∨ s | case intro.intro.inl
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
⊢ r ∨ s
case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | { have hr : r := hpr hp
left
assumption } | case intro.intro.inl
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
⊢ r ∨ s
case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
⊢ r ∨ s | case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | { have hs : s := hqs hq
right
assumption } | case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
⊢ r ∨ s | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | have hr : r := hpr hp | case intro.intro.inl
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
⊢ r ∨ s | case intro.intro.inl
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
hr : r
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | left | case intro.intro.inl
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
hr : r
⊢ r ∨ s | case intro.intro.inl.h
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
hr : r
⊢ r |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | assumption | case intro.intro.inl.h
p q r s : Prop
hpr : p → r
hqs : q → s
hp : p
hr : r
⊢ r | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | have hs : s := hqs hq | case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
⊢ r ∨ s | case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
hs : s
⊢ r ∨ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | right | case intro.intro.inr
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
hs : s
⊢ r ∨ s | case intro.intro.inr.h
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
hs : s
⊢ s |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1Sols.lean | problem_3 | [191, 1] | [201, 17] | assumption | case intro.intro.inr.h
p q r s : Prop
hpr : p → r
hqs : q → s
hq : q
hs : s
⊢ s | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2.lean | HW2.problem_1 | [80, 1] | [81, 8] | sorry | ⊢ ∃ n, ∀ (x : ℕ), n ≤ x | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2.lean | HW2.problem_2 | [126, 1] | [127, 8] | sorry | ⊢ 5 ∣ 15 | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2.lean | HW2.problem_3 | [138, 1] | [139, 8] | sorry | ⊢ ∀ (x : ℕ), x ∣ 10 → x ∣ 100 | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2.lean | HW2.problem_4 | [174, 1] | [175, 8] | sorry | a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
⊢ a ≤ b | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2.lean | HW2.bonus_challenge | [226, 1] | [227, 8] | sorry | p : Prop
⊢ ¬(p ↔ ¬p) | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | example_1 | [28, 1] | [29, 8] | sorry | p : Prop
⊢ p → p → p | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | example_1' | [41, 1] | [44, 8] | intro hp1 | p : Prop
⊢ p → p → p | p : Prop
hp1 : p
⊢ p → p |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | example_1' | [41, 1] | [44, 8] | intro hp2 | p : Prop
hp1 : p
⊢ p → p | p : Prop
hp1 hp2 : p
⊢ p |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | example_1' | [41, 1] | [44, 8] | sorry | p : Prop
hp1 hp2 : p
⊢ p | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | problem_1 | [70, 1] | [71, 8] | sorry | p q r s : Prop
⊢ p ∧ q ∧ r → p ∧ r | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | problem_2 | [94, 1] | [95, 8] | sorry | p q r s : Prop
⊢ (p → ¬q) → ¬(p ∧ q) | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw1.lean | problem_3 | [124, 1] | [125, 8] | sorry | p q r s : Prop
⊢ (p ∨ q) ∧ (p → r) ∧ (q → s) → r ∨ s | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | eliminate h1 with h4 h5 | p q r al_ac betty_beg carl_cac : Prop
h1 : al_ac ∧ (betty_beg ∨ carl_cac)
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
⊢ False | case intro
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h5 : betty_beg ∨ carl_cac
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | eliminate h5 with h6 h7 | case intro
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h5 : betty_beg ∨ carl_cac
⊢ False | case intro.inl
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h6 : betty_beg
⊢ False
case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | { have h8 : ¬ al_ac := h2 h6 contradiction } | case intro.inl
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h6 : betty_beg
⊢ False
case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
⊢ False | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | { have h9 : betty_beg := h3 h7 have h10 : ¬ al_ac := h2 h9 contradiction } | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
⊢ False | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | have h8 : ¬ al_ac := h2 h6 | case intro.inl
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h6 : betty_beg
⊢ False | case intro.inl
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h6 : betty_beg
h8 : ¬al_ac
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | contradiction | case intro.inl
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h6 : betty_beg
h8 : ¬al_ac
⊢ False | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | have h9 : betty_beg := h3 h7 | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
⊢ False | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
h9 : betty_beg
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | have h10 : ¬ al_ac := h2 h9 | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
h9 : betty_beg
⊢ False | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
h9 : betty_beg
h10 : ¬al_ac
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Demos/Lecture04.lean | Lecture04.these_are_contradictory | [170, 1] | [187, 20] | contradiction | case intro.inr
p q r al_ac betty_beg carl_cac : Prop
h2 : betty_beg → ¬al_ac
h3 : carl_cac → betty_beg
h4 : al_ac
h7 : carl_cac
h9 : betty_beg
h10 : ¬al_ac
⊢ False | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_1 | [80, 1] | [83, 11] | existsi 0 | ⊢ ∃ n, ∀ (x : ℕ), n ≤ x | ⊢ ∀ (x : ℕ), 0 ≤ x |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_1 | [80, 1] | [83, 11] | intro x | ⊢ ∀ (x : ℕ), 0 ≤ x | x : ℕ
⊢ 0 ≤ x |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_1 | [80, 1] | [83, 11] | linarith | x : ℕ
⊢ 0 ≤ x | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_2 | [125, 1] | [127, 10] | existsi 3 | ⊢ 5 ∣ 15 | ⊢ 15 = 5 * 3 |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_2 | [125, 1] | [127, 10] | numbers | ⊢ 15 = 5 * 3 | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | intro x | ⊢ ∀ (x : ℕ), x ∣ 10 → x ∣ 100 | x : ℕ
⊢ x ∣ 10 → x ∣ 100 |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | intro hxdvd | x : ℕ
⊢ x ∣ 10 → x ∣ 100 | x : ℕ
hxdvd : x ∣ 10
⊢ x ∣ 100 |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | dsimp [dvd] at hxdvd | x : ℕ
hxdvd : x ∣ 10
⊢ x ∣ 100 | x : ℕ
hxdvd : ∃ c, 10 = x * c
⊢ x ∣ 100 |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | dsimp [dvd] | x : ℕ
hxdvd : ∃ c, 10 = x * c
⊢ x ∣ 100 | x : ℕ
hxdvd : ∃ c, 10 = x * c
⊢ ∃ c, 100 = x * c |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | eliminate hxdvd with k hkx | x : ℕ
hxdvd : ∃ c, 10 = x * c
⊢ ∃ c, 100 = x * c | case intro
x k : ℕ
hkx : 10 = x * k
⊢ ∃ c, 100 = x * c |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | existsi k*10 | case intro
x k : ℕ
hkx : 10 = x * k
⊢ ∃ c, 100 = x * c | case intro
x k : ℕ
hkx : 10 = x * k
⊢ 100 = x * (k * 10) |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_3 | [152, 1] | [159, 11] | linarith | case intro
x k : ℕ
hkx : 10 = x * k
⊢ 100 = x * (k * 10) | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_4 | [218, 1] | [222, 11] | have hab2 : 2*a ≤ a + b ∨ a + b ≤ 2*b := h (a + b) | a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
⊢ a ≤ b | a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
hab2 : 2 * a ≤ a + b ∨ a + b ≤ 2 * b
⊢ a ≤ b |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_4 | [218, 1] | [222, 11] | eliminate hab2 with h1 h2 | a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
hab2 : 2 * a ≤ a + b ∨ a + b ≤ 2 * b
⊢ a ≤ b | case inl
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h1 : 2 * a ≤ a + b
⊢ a ≤ b
case inr
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h2 : a + b ≤ 2 * b
⊢ a ≤ b |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_4 | [218, 1] | [222, 11] | linarith | case inl
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h1 : 2 * a ≤ a + b
⊢ a ≤ b
case inr
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h2 : a + b ≤ 2 * b
⊢ a ≤ b | case inr
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h2 : a + b ≤ 2 * b
⊢ a ≤ b |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.problem_4 | [218, 1] | [222, 11] | linarith | case inr
a b : ℤ
h : ∀ (x : ℤ), 2 * a ≤ x ∨ x ≤ 2 * b
h2 : a + b ≤ 2 * b
⊢ a ≤ b | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | intro hiff | p : Prop
⊢ ¬(p ↔ ¬p) | p : Prop
hiff : p ↔ ¬p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | eliminate hiff with h_left h_right | p : Prop
hiff : p ↔ ¬p
⊢ False | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | have hnp : ¬ p | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
⊢ False | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
⊢ ¬p
case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | { intro hp
have hnp : ¬ p := h_left hp
contradiction } | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
⊢ ¬p
case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
⊢ False | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | have hp : p := h_right hnp | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
⊢ False | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
hp : p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | contradiction | case intro
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hnp : ¬p
hp : p
⊢ False | no goals |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | intro hp | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
⊢ ¬p | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hp : p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | have hnp : ¬ p := h_left hp | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hp : p
⊢ False | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hp : p
hnp : ¬p
⊢ False |
https://github.com/robertylewis/CS22-Lean-Dev.git | a2dd2fc7ddc1f969567b2476719b9976cd12682b | BrownCs22/Homework/Hw2sols.lean | HW2.bonus_challenge | [272, 1] | [280, 16] | contradiction | case hnp
p : Prop
h_left : p → ¬p
h_right : ¬p → p
hp : p
hnp : ¬p
⊢ False | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Complexity/BitTree.lean | Complexity.CostFunction.flatmap_bind | [28, 1] | [30, 73] | cases hg:g c <;> simp [flatMap, flip, Option.bind, hg] | θ : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
inst✝ : Zero θ
x : CostFunction α θ
f : β → Option α
g : γ → Option β
c : γ
⊢ flatMap (flip Option.bind f ∘ g) x c = flatMap g (flatMap f x) c | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Complexity/BitTree.lean | List.split'_isSome | [45, 9] | [49, 51] | simpa using List.split'_isSome tl | α : Type u_1
head✝¹ head✝ : α
tl : List α
⊢ Option.isSome (split' (head✝¹ :: head✝ :: tl)).1 = decide (length (head✝¹ :: head✝ :: tl) % 2 = 1) | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Complexity/BitTree.lean | List.split'_length_left | [51, 9] | [55, 56] | simpa using List.split'_length_left tl | α : Type u_1
head✝¹ head✝ : α
tl : List α
⊢ length (split' (head✝¹ :: head✝ :: tl)).2.1 = length (head✝¹ :: head✝ :: tl) / 2 | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Complexity/BitTree.lean | List.split'_length_right | [57, 9] | [61, 57] | simpa using List.split'_length_right tl | α : Type u_1
head✝¹ head✝ : α
tl : List α
⊢ length (split' (head✝¹ :: head✝ :: tl)).2.2 = length (head✝¹ :: head✝ :: tl) / 2 | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Complexity/BitTree.lean | HMem.Complexity.Karatsuba.eq_decide | [260, 1] | [261, 19] | cases b <;> simp | P : Prop
b : Bool
inst✝ : Decidable P
⊢ (b = decide P) = (decide (b = true) = true ↔ P) | no goals |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Encoding/Emulator.lean | HMem.Encoding.encodeSource_inj | [17, 1] | [21, 31] | cases h₀:s₀ <;> cases h₁:s₁ | s₀ s₁ : Source
⊢ encodeSource s₀ = encodeSource s₁ → s₀ = s₁ | case nil.nil
s₀ s₁ : Source
h₀ : s₀ = Source.nil
h₁ : s₁ = Source.nil
⊢ encodeSource Source.nil = encodeSource Source.nil → Source.nil = Source.nil
case nil.imm
s₀ s₁ : Source
h₀ : s₀ = Source.nil
hd✝ : Bool
tl✝ : Source
h₁ : s₁ = Source.imm hd✝ tl✝
⊢ encodeSource Source.nil = encodeSource (Source.imm hd✝ tl✝) → Source.nil = Source.imm hd✝ tl✝
case nil.idx
s₀ s₁ : Source
h₀ : s₀ = Source.nil
hd✝ tl✝ : Source
h₁ : s₁ = Source.idx hd✝ tl✝
⊢ encodeSource Source.nil = encodeSource (Source.idx hd✝ tl✝) → Source.nil = Source.idx hd✝ tl✝
case imm.nil
s₀ s₁ : Source
hd✝ : Bool
tl✝ : Source
h₀ : s₀ = Source.imm hd✝ tl✝
h₁ : s₁ = Source.nil
⊢ encodeSource (Source.imm hd✝ tl✝) = encodeSource Source.nil → Source.imm hd✝ tl✝ = Source.nil
case imm.imm
s₀ s₁ : Source
hd✝¹ : Bool
tl✝¹ : Source
h₀ : s₀ = Source.imm hd✝¹ tl✝¹
hd✝ : Bool
tl✝ : Source
h₁ : s₁ = Source.imm hd✝ tl✝
⊢ encodeSource (Source.imm hd✝¹ tl✝¹) = encodeSource (Source.imm hd✝ tl✝) → Source.imm hd✝¹ tl✝¹ = Source.imm hd✝ tl✝
case imm.idx
s₀ s₁ : Source
hd✝¹ : Bool
tl✝¹ : Source
h₀ : s₀ = Source.imm hd✝¹ tl✝¹
hd✝ tl✝ : Source
h₁ : s₁ = Source.idx hd✝ tl✝
⊢ encodeSource (Source.imm hd✝¹ tl✝¹) = encodeSource (Source.idx hd✝ tl✝) → Source.imm hd✝¹ tl✝¹ = Source.idx hd✝ tl✝
case idx.nil
s₀ s₁ hd✝ tl✝ : Source
h₀ : s₀ = Source.idx hd✝ tl✝
h₁ : s₁ = Source.nil
⊢ encodeSource (Source.idx hd✝ tl✝) = encodeSource Source.nil → Source.idx hd✝ tl✝ = Source.nil
case idx.imm
s₀ s₁ hd✝¹ tl✝¹ : Source
h₀ : s₀ = Source.idx hd✝¹ tl✝¹
hd✝ : Bool
tl✝ : Source
h₁ : s₁ = Source.imm hd✝ tl✝
⊢ encodeSource (Source.idx hd✝¹ tl✝¹) = encodeSource (Source.imm hd✝ tl✝) → Source.idx hd✝¹ tl✝¹ = Source.imm hd✝ tl✝
case idx.idx
s₀ s₁ hd✝¹ tl✝¹ : Source
h₀ : s₀ = Source.idx hd✝¹ tl✝¹
hd✝ tl✝ : Source
h₁ : s₁ = Source.idx hd✝ tl✝
⊢ encodeSource (Source.idx hd✝¹ tl✝¹) = encodeSource (Source.idx hd✝ tl✝) → Source.idx hd✝¹ tl✝¹ = Source.idx hd✝ tl✝ |
https://github.com/calcu16/lean_complexity.git | d267eb4f3952c654f130a119311692c1c1a7cd71 | HMem/Encoding/Emulator.lean | HMem.Encoding.encodeSource_inj | [17, 1] | [21, 31] | case imm.imm => simpa [encodeSource] using λ hhd htl ↦ ⟨hhd, encodeSource_inj htl⟩ | s₀ s₁ : Source
hd✝¹ : Bool
tl✝¹ : Source
h₀ : s₀ = Source.imm hd✝¹ tl✝¹
hd✝ : Bool
tl✝ : Source
h₁ : s₁ = Source.imm hd✝ tl✝
⊢ encodeSource (Source.imm hd✝¹ tl✝¹) = encodeSource (Source.imm hd✝ tl✝) → Source.imm hd✝¹ tl✝¹ = Source.imm hd✝ tl✝ | no goals |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.