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Proof step 22 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 + 1 < # zbrar, n0 < n, n0 < # zbrar, n < # zbrar, nused < # zbrar, n0 < nused, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = key

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