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Proof step 44 from proof payload-shift-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
zbrar[n] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ (∃ n0. n0 < nused ∧ (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).entry? ∧ (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key = key0) ↔ key0 ≠ key ∧ (∃ n0. ¬ nused < n0 ∧ zbrar[n0].entry? ∧ zbrar[n0].key = key0)

Rule argument

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)