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Proof step 131 from proof payload-shift-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
zbrar[n0] = mkzentry(key, adr), n + 1 < # zbrar, n < n0, n0 < # zbrar, nused < # zbrar, n < # zbrar, n < nused, sorted(zbrar, 0, nused + 1), n0 ≤ nused ⊦ zbrar[n].entry?, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key, zbrar[(n0 - 1) + 1].entry? ∧ zbrar[(n0 - 1) + 1].key = key

Rule argument

Additional information

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