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Proof step 6 from proof alignup-le-is-aligned (previous step)

m % n = 0, m < (m0 % n = 0 ⊃ m0;n * m0 / n + n) ⊦ n = 0, m < m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m % n = 0, m0 < (m0 % n = 0 ⊃ m0;n * m0 / n + n), m < (m0 % n = 0 ⊃ m0;n * m0 / n + n), m0 ≤ m ⊦ n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)