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Proof step 22 from proof valid-idx-move-last (previous step)

ar[m1] = elemindex(a0, m3), kar[m3] = key-index(key, m1), kar[m2] = key-index(key0, m1), m2 < # kar, m1 < # ar, m3 < # kar, m2 < m3, m2 + 1 < # kar, ∀ m. ¬ m3 < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m4 = m2

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: m2 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ key-index(key, m).idx = m; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic% ⊦ elemindex(a, m).idx = m; (s)% ⊦ m +1 = m + 1; (s)% ⊦ ¬ n < n; (s) Used terms: m2