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Proof step 4 from proof divi-mod (previous step)

n = m0 * m + n0, n0 < m ⊦ m | n ↔ n0 = 0, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 < m, m | m0 * m + n0 ⊦ n0 = 0

Rule argument

Additional information

Used simplifier rules: divi-mult: ⊦ m | m * n0;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 0 + m = m; (s)% ⊦ m < n → n ≠ 0; (s)