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Proof step 82 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), n0 < # avol, 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) ⊦ lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0, id-idx ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];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 ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];cleanup-lpt(lpt4, n0)), freelist + n0 ') ∧ keyset(gch) = gc-heap ((lpt4[n0].ref-size = 0 ∧ lpt4[n0].flags ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, lpt4[n0].gcheapidx)];cleanup-lpt(lpt4, n0)), [])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 83:
# 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)), [])

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt4[n0], m, m0, lpf0, m3]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt4[n0], m, m0, lpf0, m3