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Proof step 12 from proof no-dups-update-key (previous step)

kar[m1] = key-index(key0, m4), kar[m3] = key-index(key2, m4), m3 < m, m3 < # kar, m1 < m, m1 < # kar, ∀ m0, m1. m0 < # kar ∧ m0 < m ∧ m1 < # kar ∧ m1 < m ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m1 = m3

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: m1, m3

Additional information

Used simplifier rules: ⊦ key-index(key, m).idx = m; (s) Used terms: m1, m3