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Proof step 44 from proof prepost-create-gcheap (previous step)

# lpt = n1 + n0, # lpt2 = n1 + n0, # lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, n0) = keyset(gch), keyset(gch0) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt1), ∀ n. n < n1 + n0 → lpt2[n].ref-size = lpt1[n].ref-size ∧ lpt2[n].size = lpt1[n].size ∧ lpt2[n].flags = lpt1[n].flags, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0, ∀ n. n < n1 + n0 → lpt1[n].ref-size = lpt[n].ref-size ∧ lpt1[n].size = lpt[n].size ∧ lpt1[n].flags = lpt[n].flags ⊦ n1 = 0, gc-heap(lpt2, log, n0) ∪ (lpt2[n0].flags = LP_GROUP_NODES ⊃ ∅ ++ key-index(lpt2[n0].ref-size, n0);∅) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n0 ∈ log

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
# lpt1 = n1 + n0, # lpt2 = n1 + n0, # lpt = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), lpt2[n0] = mklp(m2, m3, lpf, m4), gc-heap(lpt2, log, n0) = keyset(gch), keyset(gch0) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), bin-heap-inv(gch, lpt1), bin-heap-inv(gch0, lpt), ∀ n. n < n1 + n0 → lpt1[n].ref-size = lpt[n].ref-size ∧ lpt1[n].size = lpt[n].size ∧ lpt1[n].flags = lpt[n].flags, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0, ∀ n. n < n1 + n0 → lpt2[n].ref-size = lpt1[n].ref-size ∧ lpt2[n].size = lpt1[n].size ∧ lpt2[n].flags = lpt1[n].flags ⊦ n1 = 0, gc-heap(lpt2, log, n0) ∪ (lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m2, n0);∅) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n0 ∈ log

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] → [lpt2[n0], m2, m3, lpf, m4]

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: lpt2[n0], m2, m3, lpf, m4