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Proof step 93 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n2 + n0, # avol1 = n2 + n0, # lpt4 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), lpt4[n0] = mklp(0, m1, lpf, m3), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch, lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1) ⊦ lpf = LP_FREE, lpf = LP_GROUP_NODES, n2 = 0, avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 94:
⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n])
Proof step 95:
# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt4[n0] = mklp(0, m1, lpf, m3), lpt3[n0] = mklp(0, m1, lpf, m2), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), n0 < # avol, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol1, nobuffer), awbuf-inv(avol, nobuffer), bin-heap-inv(gch0, lpt4), bin-heap-inv(gch, lpt3), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol1), synced(avol) ⊦ lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0, # avol1 = # avol[n0, unmapped] ∧ # avol1 = # lpt4 ∧ (∀ n. n < # avol1 ∧ (lpt4[n].ref-size ≠ 0 ∨ lpt4[n].flags = LP_FREE) → avol1[n] = avol[n0, unmapped][n])

Rule argument

spec: persistence-base name: avol-cleanup-lpt-unchanged seq: ⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n]) subst: [lpt, avol1, avol0] → [lpt4, avol[n0, unmapped], avol1] flags: <all paths>

Additional information

Used terms: lpt4, avol[n0, unmapped], avol1