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Proof step 20 from proof in-payload (previous step)

zbrar[m] = mkzentry(key0, adr), zbrar[(m + 1) + n].entry?, m + nused0 < # zbrar, m < # zbrar, n < nused0 ⊦ ∃ n0. ¬ nused0 < n0 ∧ zbrar[m + n0].entry? ∧ zbrar[m + n0].key = zbrar[(m + 1) + n].key

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
zbrar[m] = mkzentry(key0, adr), zbrar[(m + 1) + n] = mkzentry(key, adr0), zbrar[(m + 1) + n].entry?, n < nused0, m < # zbrar, m + nused0 < # zbrar ⊦ ∃ n0. ¬ nused0 < n0 ∧ zbrar[m + n0].entry? ∧ zbrar[m + n0].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] → [zbrar[(m + 1) + n], key, adr0]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: zbrar[(m + 1) + n], key, adr0