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Proof step 41 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 ⊦ 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

Rule argument

spec: persistence-base name: gc-heap-rec seq: ⊦ n < # lpt → gc-heap(lpt, nx, n + 1) = gc-heap(lpt, nx, n) ∪ (¬ n ∈ nx ∧ lpt[n].flags = LP_GROUP_NODES ⊃ {key-index(lpt[n].ref-size, n)} ;∅ ) subst: [n, nx, lpt] → [n0, log, lpt2] flags: <all paths>

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0, log, lpt2