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Proof step 66 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), n0 = n2 +1, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused, n ≤ n0, n0 ≤ nused ⊦ key0 = key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
zbrar[n] = mkzentry(key, adr), zbrar[n2 + 1] = mkzentry(key0, adr0), nused < # zbrar, n < # zbrar, n2 < nused, n2 + 1 < # zbrar, n2 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ n2 + 1, n ≤ nused ⊦ key0 = key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%le-one: ⊦ m ≤ n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m +1 = m + 1; (s)