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Proof step 3 from proof rounded-help (previous step)

m * n / m + m ≤ n ⊦ m = 0

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m * n0 +1 / m + m ≤ n0 +1, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ m = 0

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%n ≠ 0 ⊦ 0 / n = 0; (s)% ⊦ 0 * n = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ 0 ↔ m = 0; (s)