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Proof step 30 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), lpt2[n0] = mklp(m1, m2, lpf, m5), 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, []), 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, 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), []) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt2 ∧ # lpt2 = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n), lpt2[n0, mklp(m1, 0, LP_FREE, m5)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist + n0 ') ∧ keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ bin-heap-inv(gch1, lpt2[n0, mklp(m1, 0, LP_FREE, m5)]) ∧ # lpt2 < n1 + n), # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# 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), 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, []), # gc-heap(cleanup-lpt(lpt4, n0), []) ≠ 0, gc-heap(cleanup-lpt(lpt4, n0), []) ≠ ∅, m0 ≠ 0, n1 ≠ 0, 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, 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), []) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt2 ∧ # lpt2 = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n), lpt2[n0, mklp(0, 0, LP_FREE, m5)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist + n0 ') ∧ keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ # lpt2 < n1 + n)

Rule argument

Additional information

Used simplifier rules: id-idx-fwd-1: ⊦ lpt0[n] = mklp(n0, n1, lpf0, n2) ∧ lpt1[n] = mklp(m0, m1, lpf1, m2) ∧ n < # lpt1 ∧ id-idx(lpt0, lpt1) → n0 = m0 ∧ n1 = m1 ∧ lpf0 = lpf1; (forward) from specification gc-heap-rename%n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)