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Proof step 88 from proof payload-shift-left (previous step)

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?

User applied rule cut formula

And obtained the following new goals

Proof step 89:
zbrar[n0] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, 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?
Proof step 94:
zbrar[n0] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, 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?, n0 < n

Rule argument

fma: n0 < n

Additional information

Used formulas: n0 < n