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Proof step 1 from proof modeq-01 (conclusion)

⊦ 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;%eq: ⊦ m0 ≠ 0 → (m * m0 = n * m0 ↔ m = n);%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2