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Proof step 82 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key, adr), zbrar[n0].entry?, n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused ⊦ 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 83:
zbrar[n0] = mkzentry(key, adr), n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = payload(zbrar, 0, nused + 1)[key], zbrar[n].entry?

Rule argument

Additional information

Used simplifier rules: ⊦ mkzentry(key, adr).entry?; (s)