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Proof step 47 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, n0 < # lpt2, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch1, lpt2), bin-heap-inv(bin-heap(kar, m1), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(lpt3, lpt2), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ id-idx(lpt0, lpt1) → id-idx(lpt0[n, mklp(n0, n1, lpf, n2)], lpt1[n, mklp(n0, n1, lpf, m2)])
Proof step 49:
# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), n0 < # lpt2, 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(bin-heap(kar, m1), lpt3), bin-heap-inv(gch1, lpt2), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), id-idx(lpt3, lpt2), id-idx(cleanup-lpt(lpt4, n0), lpt2), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ true

Rule argument

spec: persistence-base name: id-idx-write-both seq: ⊦ id-idx(lpt0, lpt1) → id-idx (lpt0[n, mklp(n0, n1, lpf, n2)], lpt1[n, mklp(n0, n1, lpf, m2)]) subst: [m2, lpt1, n2, lpf, n1, n0, n, lpt0] → [m5, lpt2, m3, LP_FREE, 0, 0, n0, cleanup-lpt(lpt4, n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ id-idx(lpt0, lpt1) ∧ id-idx(lpt1, lpt2) → id-idx(lpt0, lpt2); (ss) Used terms: m5, lpt2, m3, LP_FREE, 0, 0, n0, cleanup-lpt(lpt4, n0)