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Proof step 132 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key, adr), n + 1 < # zbrar, n < n0, n0 < # zbrar, nused < # zbrar, n < # zbrar, n < nused, sorted(zbrar, 0, nused + 1), n0 ≤ nused ⊦ zbrar[n].entry?, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key, zbrar[(n0 - 1) + 1].entry? ∧ zbrar[(n0 - 1) + 1].key = key

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] → [n0, m]

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 + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m +1 = m + 1; (s)% ⊦ mkzentry(key, adr).entry?; (s)% ⊦ mkzentry(key, adr).key = key; (s)% ⊦ 0 ≤ m; (s)% ⊦ ¬ m < 0; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n0, m