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Proof step 12 from proof valid-idx-update-key (previous step)

kar[m] = key-index(key0, m0), ar[m2] = elemindex(a, m3), kar[m1] = key-index(key1, m2), m1 < n, m1 < # kar, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m1 = m, m2 < # ar ∧ m3 = m1

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: m1

Additional information

Used simplifier rules: 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)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ elemindex(a, m).idx = m; (s) Used terms: m1