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Proof step 27 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, 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, n0 < n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 < # zbrar, n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ n0, 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: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)