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Proof step 8 from proof no-dups-idx-mvlast (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)% ⊦ ¬ n < n; (s)% ⊦ key-index(key, m).idx = m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic Used terms: m1, m