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Proof step 45 from proof inv-format (previous step)

awbuf-inv(fill(mkavolume(m3), unmapped), nobuffer), freelist-cons(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), freelist), synced(fill(mkavolume(m3), unmapped)) ⊦ bin-heap-inv(bin-heap(mkkeyarray(1), 0), fill(mklparray(m3), mklp(0, 0, LP_FREE, 0))) ∧ lpt-leb-size(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size)
Proof step 47:
awbuf-inv(fill(mkavolume(m3), unmapped), nobuffer), freelist-cons(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), freelist), synced(fill(mkavolume(m3), unmapped)) ⊦ ( bin-heap(mkkeyarray(1), 0).size ≤ # bin-heap(mkkeyarray(1), 0).ar ∧ no-dups-idx(bin-heap(mkkeyarray(1), 0).ar, bin-heap(mkkeyarray(1), 0).size) ∧ valid-idx(bin-heap(mkkeyarray(1), 0).ar, fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), bin-heap(mkkeyarray(1), 0).size) ∧ 2exp-size(# bin-heap(mkkeyarray(1), 0).ar) ∧ heap-order(bin-heap(mkkeyarray(1), 0).ar, bin-heap(mkkeyarray(1), 0).size)) ∧ lpt-leb-size(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)))

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: bin-heap-inv-def seq: ⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) subst: [lpt, bh] → [fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), bin-heap(mkkeyarray(1), 0)] flags: <all paths>

Additional information

Used terms: fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), bin-heap(mkkeyarray(1), 0)