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Proof step 3 from proof valid-idx-last-valid (previous step)

kar[m] = key-index(key, n), m < m0, m < # kar, # ar ≤ n, m0 ≤ # kar, ∀ m. m < m0 → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: m abort: F discard: T computed: T

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%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)% ⊦ ¬ n < n; (s) Used terms: m