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Proof step 48 from proof payload-shift-left (previous step)

(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]) = mkzentry(key0, adr0), zbrar[n] = 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 ⊦ key0 ≠ key ∧ (∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]) = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ key0 ≠ key ∧ (∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkzentry(key, adr).entry?; (s)