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Proof step 62 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n0 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), n ≤ nused, 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 63:
zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 + 1 < # zbrar, n0 < n, n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, sorted(zbrar, 0, nused + 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)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic