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Proof step 20 from proof process-queue (previous step)

((del-list(to_delete, m + 1) * P))(H), ((del-list(to_delete0, m) * P))(H0), ((del-list(to_delete1, m - 1) * P))(H1), 1 ≤ m ⊦ m = 0, ((del-list(to_delete1, m + 1 - 2) * P))(H1)

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m0]

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m0