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Proof step 35 from proof payload-shift-left (previous step)

zbrar[n2 + 1] = mkzentry((n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key, adr0), zbrar[n] = mkzentry(key, adr), (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).entry?, n0 + 1 < # zbrar, n < # zbrar, nused < # zbrar, n2 < nused, n2 + 1 < # zbrar, n2 < # zbrar, n0 < n2, n < nused, n0 < nused, n0 < # zbrar, n0 + 1 < nused, n + 1 < # zbrar, 2 + n0 < # zbrar, sorted(zbrar, 0, nused + 1), (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ n2, n ≤ n2 + 1, ∀ n1. ¬ n2 < n1 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key ⊦ (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key = key, payload(shl(zbrar, n, nused + 1), 0, nused)[(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key] = adr0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]) = mkzentry(key0, adr1), zbrar[n] = mkzentry(key, adr), zbrar[n2 + 1] = mkzentry(key0, adr0), (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).entry?, 2 + n0 < # zbrar, n + 1 < # zbrar, n0 + 1 < nused, n0 < # zbrar, n0 < nused, n < nused, n0 < n2, n2 < # zbrar, n2 + 1 < # zbrar, n2 < nused, nused < # zbrar, n < # zbrar, n0 + 1 < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ n2 + 1, n ≤ n2, ∀ n1. ¬ n2 < n1 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = 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]), key0, adr1]

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]), key0, adr1