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Proof step 49 from proof prepost-resize (previous step)

2exp-size(n0), 2exp-size(# kar), m < minsize, m < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ heap-order(copy(kar, 0, mkkeyarray(n0), 0, m), m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ heap-order(kar, n) ↔ (∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key)
Proof step 51:
2exp-size(# kar), 2exp-size(n0), m < n0, m < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦ ∀ m0. m0 < m ∧ m0 ≠ 0 → ¬ copy(kar, 0, mkkeyarray(n0), 0, m)[m0].key < copy(kar, 0, mkkeyarray(n0), 0, m)[(m0 - 1) / 2].key

Rule argument

spec: bin-min-heap-inv name: heap-order seq: ⊦ heap-order(kar, n) ↔ (∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key) subst: [n, kar] → [m, copy(kar, 0, mkkeyarray(n0), 0, m)] flags: <all paths>

Additional information

Used terms: m, copy(kar, 0, mkkeyarray(n0), 0, m)