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Proof step 73 from proof prepost-cleanup-lpt (previous step)

# avol1 = # lpt4, # lpt3 = # lpt4, lpt3[n0].ref-size = 0, keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), lpt3[n0].flags ≠ LP_FREE, lpt3[n0].flags ≠ LP_GROUP_NODES, n0 < # lpt4, 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) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n1 := n0 + 1⟫ ( n1 ≤ # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n1), lpt3[n0, mklp(lpt3[n0].ref-size, 0, LP_FREE, lpt3[n0].gcheapidx)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n1), freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n1), []) ∧ bin-heap-inv(gch, lpt3[n0, mklp(lpt3[n0].ref-size, 0, LP_FREE, lpt3[n0].gcheapidx)]) ∧ # lpt4 < (# lpt4 - n0) + n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 74:
# lpt3 = # lpt4, # avol1 = # lpt4, # lpt4 = n2 + n0, lpt3[n0].ref-size = 0, keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # lpt4, 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), n0 ≤ # lpt4 ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n1 := n0 + 1⟫ ( n1 ≤ # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n1), lpt3[n0, mklp(lpt3[n0].ref-size, 0, LP_FREE, lpt3[n0].gcheapidx)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n1), freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n1), []) ∧ bin-heap-inv(gch, lpt3[n0, mklp(lpt3[n0].ref-size, 0, LP_FREE, lpt3[n0].gcheapidx)]) ∧ # lpt4 < n2 + n1), lpt3[n0].flags = LP_FREE, lpt3[n0].flags = LP_GROUP_NODES

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0, # lpt4, n]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0, # lpt4, n