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Proof step 52 from proof initialization (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)) ⊦ abs-istore(fill(mkavolume(m3), unmapped), fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), ∅) ∧ abs-gstore(fill(mkavolume(m3), unmapped), fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), ∅, ∅) ∧ flash-lpt-cons(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), ∅, ∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size))
Proof step 54:
awbuf-inv(fill(mkavolume(m3), unmapped), nobuffer), freelist-cons(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), freelist), synced(fill(mkavolume(m3), unmapped)) ⊦ (∀ n. (n < # fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)) ∧ fill(mklparray(m3), mklp(0, 0, LP_FREE, 0))[n].flags = LP_INDEX_NODES ↔ n ∈ ∅) ∧ ( n ∈ ∅ → abs-leb(fill(mkavolume(m3), unmapped)[n], (∅)[n], fill(mklparray(m3), mklp(0, 0, LP_FREE, 0))[n]) ∧ fill(mklparray(m3), mklp(0, 0, LP_FREE, 0))[n].ref-size = (∅)[n].ref-size)) ∧ abs-gstore(fill(mkavolume(m3), unmapped), fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), ∅, ∅) ∧ flash-lpt-cons(fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), ∅, ∅)

Rule argument

spec: persistence-base name: abs-istore-def seq: ⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. ( n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ ( n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size)) subst: [istore, lpt, avol] → [∅, fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), fill(mkavolume(m3), unmapped)] flags: <all paths>

Additional information

Used terms: ∅, fill(mklparray(m3), mklp(0, 0, LP_FREE, 0)), fill(mkavolume(m3), unmapped)