lean2/tests/lean/induction1.lean.expected.out

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Set: pp::colors
Set: pp::unicode
Imported 'macros'
Using: Nat
Assumed: Induction
Proved: Comm1
Proved: Comm2
theorem Comm2 : ∀ n m : , n + m = m + n :=
forall::intro
(λ n : ,
Induction ◂ (λ x : , n + x == x + n) ◂ (Nat::add::zeror n ⋈ symm (Nat::add::zerol n)) ◂
forall::intro
(λ m : ,
discharge
(λ iH : n + m = m + n,
Nat::add::succr n m ⋈ subst (refl (n + m + 1)) iH ⋈ symm (Nat::add::succl m n))))