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Proof step 37 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(m, m0, lpf, 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(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 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, keyset(gch1) = gc-heap((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), []) ∧ freelist-cons((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), freelist + n0 ') ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ id-idx((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), lpt2[n0, mklp(0, 0, LP_FREE, m5)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# 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(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 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], []) ∧ freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

Rule argument

Additional information

Used simplifier rules: id-idx-cleanup-lpt-backwards-fwd: n < # lpt0 ⊦ id-idx(cleanup-lpt(lpt0, n), lpt1) ∧ lpt0[n] = mklp(m0, m1, lpf0, m2) ∧ lpt1[n] = mklp(n0, n1, lpf1, n2) → m0 = n0 ∧ m1 = n1 ∧ lpf0 = lpf1;% ⊦ LP_FREE ≠ LP_GROUP_NODES; (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)