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

n0 = n2 + n1, n1 ≤ n0 ⊦ n0 - n1 + (n2 % n = 0 ⊃ n2;n2 / n * n) = n2 % n, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ n2 - (n2 % n = 0 ⊃ n2;n2 / n * n) = n2 % n, n = 0

Rule argument

Additional information

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