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Proof step 4 from proof addle-01 (previous step)

m * n1 = (m * m1 + m) + n0, n1 ≤ m1, ∀ m, n1, n0. m * n1 = m * m1 + n0 ∧ n1 < m1 → m = 0 ⊦ m = 0

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: m, n1, n0 + m

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%eq: ⊦ m = m + n ↔ n = 0; from specification nat-basic2%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2 Used terms: m, n1, n0 + m