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Proof step 38 from proof prepost-create-gcheap (previous step)

# lpt = 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), id-idx(lpt2, lpt1), ∀ 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 ⊦ gc-heap(lpt2, log, n0 + 1) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n1 = 0, n0 ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ 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)
Proof step 40:
# lpt1 = # lpt2, # lpt1 = n1 + n0, # lpt = 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(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 < # lpt1 → lpt2[n].ref-size = lpt1[n].ref-size ∧ lpt2[n].size = lpt1[n].size ∧ lpt2[n].flags = lpt1[n].flags ⊦ gc-heap(lpt2, log, n0 + 1) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n1 = 0, n0 ∈ log

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] → [lpt1, lpt2] flags: <all paths>

Additional information

Used terms: lpt1, lpt2