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Proof step 114 from proof payload-shift-left (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 115:
(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]) = mkzentry(key, adr), (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).entry?, n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[n].entry?, ∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key

Rule argument

spec: zbranch name: elim-03 seq: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)) subst: [zbr, key, adr] → [(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]), key, adr]

Additional information

Used simplifier rules: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]), key, adr