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Proof step 58 from proof payload-shift-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
zbrar[n] = mkzentry(key, adr), zbrar[n0].entry?, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused, n0 ≤ nused ⊦ zbrar[n0].key = key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[n0].key

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)