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Proof step 2 from proof two-succ-06 (previous step)

2 * m = 2 * n + m0, m < n ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ m, m0. ¬(2 * m = 2 * n0 + m0 ∧ m < n0), 2 * m = 2 * n0 +1 + m0, m < n0 +1 ⊦

Rule argument

term: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%z: ⊦ 0 + m = m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%less-1: ⊦ ¬ n < 0; from specification nat-basic1