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Proof step 14 from proof no-dups-idx-mvlast (previous step)

kar[m2] = key-index(key0, m3), kar[m1] = key-index(key, m3), m1 + 1 < # kar, m2 < # kar, m2 + 1 < # kar, m < # kar, m1 < # kar, m1 < m, m2 < m, ∀ m1, m2. m1 < # kar ∧ ¬ m < m1 ∧ m2 < # kar ∧ ¬ m < m2 ∧ m1 ≠ m2 → kar[m1].idx ≠ kar[m2].idx ⊦ m1 = m0, m1 = m2, m2 = m0

User applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: m2, m1 abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)% ⊦ key-index(key, m).idx = m; (s) Used terms: m2, m1