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Proof step 31 from proof keys-shift-left (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 32:
n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ nused ⊦ zbrar[n0].key = zbrar[n].key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[n0].key
Proof step 34:
n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ nused ⊦ zbrar[n0].key = zbrar[n].key, n0 < n, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[n0].key

Rule argument

fma: n0 < n

Additional information

Used formulas: n0 < n