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Proof step 83 from proof prepost-cleanup-lpt (previous step)

# lpt3 = n2 + n0, # avol1 = n2 + n0, # lpt4 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), lpt4[n0] = mklp(m, m0, lpf0, m3), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, 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) ⊦ lpf = LP_FREE, lpf = LP_GROUP_NODES, n2 = 0, id-idx((m = 0 ∧ lpf0 ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), lpt3[n0, mklp(0, 0, LP_FREE, m2)]) ∧ awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ freelist-cons((m = 0 ∧ lpf0 ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), freelist + n0 ') ∧ keyset(gch) = gc-heap((m = 0 ∧ lpf0 ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)];cleanup-lpt(lpt4, n0)), [])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
# lpt3 = n2 + n0, # avol1 = n2 + n0, # lpt4 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), lpt4[n0] = mklp(0, m1, lpf, m3), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, 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) ⊦ lpf = LP_FREE, lpf = LP_GROUP_NODES, n2 = 0, awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], [])

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;%⊦ id-idx(lpt0, lpt1) → id-idx (lpt0[n, mklp(n0, n1, lpf, n2)], lpt1[n, mklp(n0, n1, lpf, m2)]); (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)