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Proof step 14 from proof keys-shift-left (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 15:
(n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key = zbrar[n].key, n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦
Proof step 27:
n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ ∃ n1. ¬ nused < n1 ∧ zbrar[n1].key = (n0 < n ⊃ zbrar[n0];zbrar[n0 + 1]).key

Rule argument

pos: right 1

Proof step 14 from proof keys-shift-left (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information