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Proof step 33 from proof prepost-gcheap-add-log (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt, lpt1] flags: <all paths>

Additional information

Used terms: lpt, lpt1