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Proof step 54 from proof prepost-resize (previous step)

2exp-size(# kar), 2exp-size(n0), m1 + 1 < # kar, m1 + 1 < minsize, m < n0, m < minsize, m1 + 1 < m, copy(kar, 0, mkkeyarray(n0), 0, m)[m1 + 1].key < copy(kar, 0, mkkeyarray(n0), 0, m)[m1 / 2].key, m1 + 1 < n0, 2 + m1 < n0, 2 + m1 < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
copy(kar, 0, mkkeyarray(n0), 0, m)[m1 + 1] = key-index(key, m0), 2exp-size(n0), 2exp-size(# kar), 2 + m1 < minsize, 2 + m1 < n0, m1 + 1 < n0, key < copy(kar, 0, mkkeyarray(n0), 0, m)[m1 / 2].key, m1 + 1 < m, m < minsize, m < n0, m1 + 1 < minsize, m1 + 1 < # kar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦

Rule argument

spec: key-index name: elim seq: ⊦ key = ki.key ∧ m = ki.idx ↔ ki = key-index(key, m) subst: [ki, key, m] → [copy(kar, 0, mkkeyarray(n0), 0, m)[m1 + 1], key, m0]

Additional information

Used simplifier rules: ⊦ key = ki.key ∧ m = ki.idx ↔ ki = key-index(key, m); (elim) Used terms: copy(kar, 0, mkkeyarray(n0), 0, m)[m1 + 1], key, m0