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Proof step 2 from proof modeq-01 (previous step)

n0 < n ⊦ m * n + n0 = m0 * n ↔ m = m0 ∧ n0 = 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: mod-neq-02: ⊦ n0 < n ∧ n0 ≠ 0 → m * n ≠ m0 * n + n0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%zero-02: ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 0 + m = m; (s)