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Proof step 113 from proof prepost-cleanup-lpt (previous step)

# avol1 = # lpt4, # lpt3 = # lpt4, lpt4[n0] = mklp(m, m0, lpf, m1), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), 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) ⊦ lpt3[n0].ref-size = 0 ∧ lpt3[n0].flags ≠ LP_FREE, id-idx((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m1)];cleanup-lpt(lpt4, n0)), lpt3) ∧ freelist-cons((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m1)];cleanup-lpt(lpt4, n0)), freelist) ∧ keyset(gch) = gc-heap((m = 0 ∧ lpf ≠ LP_FREE ⊃ cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m1)];cleanup-lpt(lpt4, n0)), [])

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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] → [lpt3[n0], m2, m3, lpf0, m4]

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;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt3[n0], m2, m3, lpf0, m4