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Proof step 124 from proof payload-shift-left (previous step)

zbrar[n0] = mkzentry(key, adr), n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ nused ⊦ zbrar[n].entry?, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key

User applied rule cut formula

And obtained the following new goals

Proof step 125:
zbrar[n0] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n0 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), n ≤ nused, n0 ≤ nused ⊦ zbrar[n].entry?, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key
Proof step 127:
zbrar[n0] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused, n0 ≤ nused ⊦ zbrar[n].entry?, n0 < n, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).entry? ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = key

Rule argument

fma: n0 < n

Additional information

Used formulas: n0 < n