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Proof step 7 from proof le (previous step)

m ≤ n ⊦ m0 = 0, m0 * m ≤ m0 * n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
m0 * n < m0 * m, m ≤ n ⊦ m = 0, m0 = 0

Rule argument

Additional information

Used simplifier rules: zero-01: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)