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Proof step 80 from proof payload-shift-left (previous step)

nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, 0 + nused + 1 ≤ # zbrar, ∃ n. n < nused + 1 ∧ zbrar[0 + n].entry? ∧ zbrar[0 + n].key = key ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = payload(zbrar, 0, nused + 1)[key], zbrar[n].entry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
zbrar[n0].entry?, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), zbrar[n0].key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[zbrar[n0].key] = payload(zbrar, 0, nused + 1)[zbrar[n0].key], zbrar[n].entry?

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + 1 ≤ n ↔ m < n; (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)