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Proof step 48 from proof abs-istore-crash (previous step)

# avol0 = # lpt, # lpt0 = # lpt, istore0[n] = indexblock(indx1, lax2, m0), istore[n] = indexblock(indx0, lax0, m3), lpt[n] = mklp(m3, m5, LP_INDEX_NODES, m6), (∅)[n] = groupblock(gndx, lax1, m7), lpt0[n] = mklp(m0, m10, LP_INDEX_NODES, m2), dom istore ∩ elems nx = ∅, n < # lpt, abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m3, m5, LP_INDEX_NODES, m6)), synced(avol0), avol1 ↓ avol0, n ∈ istore, n ∈ istore0, istore0 ⊑ istore, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0 ⊦ m0 = 0, abs-leb(avol1[n], indexblock(indx0, lax0, m0), mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2)), n ∈ gstore0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n])
Proof step 50:
# avol1 = # avol0, # lpt0 = # lpt, # avol0 = # lpt, lpt0[n] = mklp(m0, m10, LP_INDEX_NODES, m2), (∅)[n] = groupblock(gndx, lax1, m7), lpt[n] = mklp(m3, m5, LP_INDEX_NODES, m6), istore[n] = indexblock(indx0, lax0, m3), istore0[n] = indexblock(indx1, lax2, m0), dom istore ∩ elems nx = ∅, n < # lpt, abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m3, m5, LP_INDEX_NODES, m6)), synced(avol0), n ∈ istore0, n ∈ istore, istore0 ⊑ istore, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0, ∀ n. n < # avol0 → avol1[n] ↓ avol0[n] ⊦ m0 = 0, abs-leb(avol1[n], indexblock(indx0, lax0, m0), mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2)), n ∈ gstore0

Rule argument

spec: awbuf-inv name: down-arrow-def seq: ⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n]) subst: [avol0, avol1] → [avol0, avol1] flags: <all paths>

Additional information

Used terms: avol0, avol1