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Proof step 87 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key, adr), zbrar[0 + n0] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n0 < # zbrar, n0 < nused + 1, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused, 0 + nused + 1 ≤ # zbrar, ∀ n1. n1 < n0 ∧ zbrar[0 + n1].entry? → zbrar[0 + 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 88:
zbrar[n0] = mkzentry(key, adr), n0 < # zbrar, n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = adr, zbrar[n].entry?

Rule argument

Additional information

Used simplifier rules: m0 < m, m1 < m, m ≤ # zbrar ⊦ sorted(zbrar, 0, m) ∧ zbrar[m0] = mkzentry(key, adr0) → (zbrar[m1] = mkzentry(key, adr1) ↔ m0 = m1 ∧ adr0 = adr1); (ws)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ 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% ⊦ n + 0 = n; (s)