16 lines
559 B
Text
16 lines
559 B
Text
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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forall::intro
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(λ n : ℕ,
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Induction ◂ (λ x : ℕ, n + x == x + n) ◂ (Nat::add::zeror n ⋈ symm (Nat::add::zerol n)) ◂
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forall::intro
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(λ m : ℕ,
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discharge
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(λ iH : n + m = m + n,
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Nat::add::succr n m ⋈ subst (refl (n + m + 1)) iH ⋈ symm (Nat::add::succl m n))))
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