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Proof step 96 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key, adr), n0 = n2 +1, nused < # zbrar, n < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n ≤ n0, n0 ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = adr, zbrar[n].entry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
zbrar[n2 + 1] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n2 < nused, n2 + 1 < # zbrar, n2 < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ n2 + 1, n ≤ nused, ∀ n0. ¬ n2 < n0 ∧ zbrar[n0].entry? → zbrar[n0].key ≠ key ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = adr, zbrar[n].entry?

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% ⊦ m < n + 1 ↔ ¬ n < m; (s)%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)