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

((n0 % n = 0 ⊃ n0;n0 / n * n) + n1) % n = 0 ⊦ (n0 % n = 0 ⊃ n0;n0 / n * n) + n1 = (n0 % n = 0 ⊃ n0;n0 / n * n) + (n1 % n = 0 ⊃ n1;n1 / n * n), n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
((n0 % n = 0 ⊃ n0;n0 / n * n) + n1) % n = 0 ⊦ n = 0, n1 = (n1 % n = 0 ⊃ n1;n1 / n * n)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)