25 lines
569 B
Text
25 lines
569 B
Text
import data.nat
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open nat algebra
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example (a b c d : nat) : a + b = 0 → b = 0 → c + 1 + a = 1 → d = c - 1 → d = 0 :=
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begin
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intro h₁ h₂,
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have aeq0 : a = 0, begin
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rewrite h₂ at h₁,
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exact h₁
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end,
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intro h₃ h₄,
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have deq0 : d = 0, begin
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have ceq : c = 0, begin
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rewrite aeq0 at h₃,
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rewrite add_zero at h₃,
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rewrite add_succ at h₃,
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krewrite add_zero at h₃,
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injection h₃, exact a_1
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end,
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rewrite ceq at h₄,
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repeat (esimp [sub, pred] at h₄),
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exact h₄
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end,
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exact deq0
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end
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