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Proof step 66 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m3, LP_GROUP_NODES, m4), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), 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, m0), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), 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 ≤ n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m0 = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt2, lpt3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: lpt2, lpt3