43 lines
1.2 KiB
Text
43 lines
1.2 KiB
Text
import data.examples.vector
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open nat vector
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example (a b : nat) : succ a = succ b → a + 2 = b + 2 :=
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begin
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intro H,
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injection H with aeqb,
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rewrite aeqb
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end
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example (A : Type) (n : nat) (v w : vector A n) (a : A) (b : A) :
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a :: v = a :: w → b :: v = b :: w :=
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begin
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intro H, injection H with veqw,
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rewrite veqw
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end
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example (A : Type) (n : nat) (v w : vector A n) (a : A) (b : A) :
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a :: v = b :: w → b :: v = a :: w :=
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begin
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intro H, injection H with aeqb veqw,
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rewrite [aeqb, veqw]
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end
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example (A : Type) (a₁ a₂ a₃ b₁ b₂ b₃ : A) : (a₁, a₂, a₃) = (b₁, b₂, b₃) → b₁ = a₁ :=
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begin
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intro H, injection H with a₁b₁ a₂b₂ a₃b₃,
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rewrite a₁b₁
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end
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example (A : Type) (a₁ a₂ a₃ b₁ b₂ b₃ : A) : (a₁ :: [], a₂, a₃) = (b₁ :: [], b₂, b₃) → b₁ = a₁ :=
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begin
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intro H, injection H with a₁b₁ a₂b₂ a₃b₃,
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rewrite a₁b₁
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end
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example (a₁ a₂ a₃ b₁ b₂ b₃ : nat) : (a₁+2, a₂+3, a₃+1) = (b₁+2, b₂+2, b₃+2) → b₁ = a₁ ∧ a₃ = b₃+1 ∧ b₂ = succ a₂ :=
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begin
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intro H, injection H with a₁b₁ sa₂b₂ a₃sb₃,
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esimp at *,
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rewrite [a₁b₁, a₃sb₃, sa₂b₂],
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repeat (split | esimp)
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end
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