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Proof step 47 from proof prepost-resize (previous step)

ar[m1] = elemindex(a, m2), kar[m0] = key-index(key, m1), 2exp-size(n0), 2exp-size(# kar), m1 < # ar, m0 + 1 < n0, m0 + 1 < minsize, m < minsize, m < n0, m0 < m, m0 < minsize, m0 < # kar, m0 < n0, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, minsize ≤ n0, ∀ m0. m0 < m → kar[m0].idx < # ar ∧ ar[kar[m0].idx].idx = m0 ⊦ m2 = m0

User applied rule all left

And closed the goal!

Rule argument

pos: left 18 terms: m0 abort: F discard: T computed: T

Additional information

Used simplifier rules: lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ key-index(key, m).idx = m; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%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: m0