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Proof step 46 from proof prepost-gcheap-add-log (previous step)

# lpt = # lpt1, lpt0[n] = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, LP_GROUP_NODES, m1), lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m5), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch1) = gc-heap(lpt1, nx0) ++ key-index(m, n0), n0 < # lpt1, bin-heap-inv(gch1, lpt0), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt, lpt0), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ ki. ki ∈ gc-heap(lpt1, nx0) → ki.idx ≠ n0 ⊦ dups(nx), dups(nx0), n0 ∈ nx0, key-index(m, n0) ∈ gc-heap(lpt1, nx0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx) ↔ n1 < # lpt ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES

Rule argument

spec: persistence-base name: gc-heap-in seq: ⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx) ↔ n1 < # lpt ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES subst: [nx, lpt, n1, n0] → [nx0, lpt1, n0, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s) Used terms: nx0, lpt1, n0, m