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Proof step 36 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 ⊦ valid-idx(copy(kar, 0, mkkeyarray(n0), 0, m), ar, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ valid-idx(kar, ar, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m)
Proof step 38:
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 ⊦ m ≤ # copy(kar, 0, mkkeyarray(n0), 0, m) ∧ (∀ m0. m0 < m → copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx < # ar ∧ ar[copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx].idx = m0)

Rule argument

spec: bin-min-heap-inv name: valid-idx seq: ⊦ valid-idx(kar, ar, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m) subst: [n, ar, kar] → [m, ar, copy(kar, 0, mkkeyarray(n0), 0, m)] flags: <all paths>

Additional information

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