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Proof step 7 from proof divi-dist (previous step)

n0 < n, m | n, m | n0, n0 < n ⊦ n = 0, m | n - n0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat inst: name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, n0, n1] flags:

Additional information

Used simplifier rules: divi-add: ⊦ m | n → (m | n + n0 ↔ m | n0);%lels-03: ⊦ m < n → m ≤ n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, n0, n1