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Proof step 21 from proof keys-shift-left (previous step)

zbrar[n0].key = zbrar[n].key, n0 + 1 < # zbrar, n0 < nused, n < # zbrar, n0 < # zbrar, n0 < n, nused < # zbrar, n ≤ nused, ∀ m, m0. m < m0 ∧ ¬ nused < m0 → zbrar[m].key < zbrar[m0].key ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: n0, n abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)%lel: ⊦ key < key0 ∧ key = key1 → key1 < key0; (forward) from specification oelem[key-order]% ⊦ ¬ key < key; (s) Used terms: n0, n