2014-01-07 18:18:31 +00:00
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Set: pp::colors
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Set: pp::unicode
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Imported 'macros'
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Using: Nat
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Assumed: Induction
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Proved: Comm1
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Proved: Comm2
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theorem Comm2 : ∀ n m : ℕ, n + m = m + n :=
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2014-01-08 08:38:39 +00:00
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λ n : ℕ,
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Induction
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2014-01-16 00:35:33 +00:00
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(λ x : ℕ, n + x = x + n)
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2014-01-19 05:11:12 +00:00
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(trans (Nat::add_zeror n) (symm (Nat::add_zerol n)))
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2014-01-08 08:38:39 +00:00
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(λ (m : ℕ) (iH : n + m = m + n),
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2014-01-19 05:11:12 +00:00
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trans (trans (Nat::add_succr n m) (subst (refl (n + m + 1)) iH)) (symm (Nat::add_succl m n)))
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