22 lines
508 B
Text
22 lines
508 B
Text
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open eq.ops
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theorem trans {A : Type} {a b c : A} (h₁ : a = b) (h₂ : b = c) : a = c :=
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begin
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cases h₁, cases h₂, apply rfl
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end
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theorem symm {A : Type} {a b : A} (h₁ : a = b) : b = a :=
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begin
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cases h₁, apply rfl
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end
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theorem congr {A B : Type} (f : A → B) {a₁ a₂ : A} (h : a₁ = a₂) : f a₁ = f a₂ :=
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begin
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cases h, apply rfl
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end
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definition inv_pV_2 {A : Type} {x y z : A} (p : x = y) (q : z = y) : (p ⬝ q⁻¹)⁻¹ = q ⬝ p⁻¹ :=
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begin
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cases p, cases q, apply rfl
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end
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