27 lines
667 B
Text
27 lines
667 B
Text
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open nat
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example (a b : nat) (P : nat → Prop) (H₁ : a = b) (H₂ : P a) : P b :=
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begin
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rewrite H₁ at *,
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exact H₂
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end
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example (a b : nat) (P : nat → Prop) (H₀ : a = 0 → b = 1) (H₁ : a = 0) (H₂ : P b) : P 1 :=
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begin
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rewrite (H₀ H₁) at *,
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exact H₂
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end
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example (a c : nat) (P : nat → Prop) (H₁ : P a) (b : nat) (H₂ : a = b) (H₃ : b = c) : P c :=
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begin
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rewrite H₂ at H₁,
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exact (eq.rec_on H₃ H₁)
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end
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example (a c : nat) (f : nat → nat → nat) (P : nat → Prop) (H₁ : P a) (b : nat) (d : nat) (H₂ : a = f b d) (H₃ : f b d = c)
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: P c :=
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begin
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rewrite H₂ at H₁,
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exact (eq.rec_on H₃ H₁)
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end
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