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Proof step 7 from proof le-same (previous step)

(m + m * n -1) + n0 ≤ m, n0 ≤ m ⊦ m = 0, n = 0, n = 1 ∧ n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n - 1 = 0 ⊦ n = 1, n = 0, m = 0

Rule argument

Additional information

Used simplifier rules: zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0);%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%lez: ⊦ 0 ≤ m; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%le-add: ⊦ m + m0 ≤ m ↔ m0 = 0; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%pred-03: ⊦ n -1 = n - 1; from specification nat