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Proof step 6 from proof valid-idx-outofbounds (previous step)

ar[m0] = elemindex(a, m1), key-index(key, m0) = kar[m2], m2 + 1 < # kar, m2 < m, m < # kar, m2 < # kar, m2 < m1, m ≤ m1, ∀ m2. ¬ m < m2 → kar[m2].idx < # ar ∧ ar[kar[m2].idx].idx = m2 ⊦ # keyset(kar, m) = 0, keyset(kar, m) = ∅

User applied rule all left

And closed the goal!

Rule argument

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

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%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%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