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Proof step 85 from proof payload-shift-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
zbrar[n0] = mkzentry(zbrar[n1].key, adr), zbrar[n1].entry?, n1 + 1 < # zbrar, n0 < # zbrar, nused < # zbrar, n < # zbrar, n1 < n0, n1 < # zbrar, n1 < nused, sorted(zbrar, 0, nused + 1), zbrar[n1].key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[zbrar[n1].key] = payload(zbrar, 0, nused + 1)[zbrar[n1].key], zbrar[n].entry?

Rule argument

Additional information

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