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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