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Proof step 5 from proof mod-le-03 (previous step)

m = m / n * n + m % n, n ≤ m % n ⊦ n = 0

User applied rule cut formula

And obtained the following new goals

Proof step 6:
n + m / n * n ≤ m, m = m / n * n + m % n, n ≤ m % n ⊦ n = 0

Rule argument

fma: n + m / n * n ≤ m

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used formulas: n + m / n * n ≤ m