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Proof step 5 from proof aligndown-add-same (previous step)

n0 + n1 = m0 * m + n2, n2 < m ⊦ (n2 = 0 ⊃ n0 + n1;m0 * m) = (n0 % m = 0 ⊃ n0;n0 / m * m) ↔ n0 % m + n1 < m, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n0 + n1 = m0 * m + n2, n2 < m ⊦ (n2 = 0 ⊃ n0 + n1;m0 * m) = (n0 % m = 0 ⊃ n0;n0 / m * m) ↔ n0 % m + n1 < m

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)