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Proof step 8 from proof valid-idx-imp-1 (previous step)

kar[m] = key-index(key, m0), ar[m0] = elemindex(a, m1), m < # kar, m < n, n < # kar, m + 1 < # kar, ∀ m. ¬ n < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m0 < # ar ∧ m1 = m

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: m abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ key-index(key, m).idx = m; (s)% ⊦ m < n → n ≠ 0; (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) Used terms: m