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Proof step 25 from proof prepost-resize (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
copy(kar, 0, mkkeyarray(n0), 0, m)[m1] = key-index(key, m2), copy(kar, 0, mkkeyarray(n0), 0, m)[m0] = key-index(key0, m2), 2exp-size(# kar), 2exp-size(n0), m0 < # kar, m0 < n0, m0 < minsize, m1 < m, m1 < n0, m < n0, m < minsize, m0 < m, m1 + 1 < minsize, m1 < # kar, m1 < minsize, m0 + 1 < minsize, m1 + 1 < n0, m0 + 1 < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦ m1 = m0

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)[m0], key0, m2]

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)[m0], key0, m2