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Proof step 51 from proof prepost-create-gcheap (previous step)

lpt1[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt2, log, n0) = keyset(gch), n0 < # lpt1, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1) ⊦ gc-heap(lpt2, log, n0 + 1) = gc-heap(lpt2, log, n0), lpf = LP_GROUP_NODES ∧ ¬ n0 ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ 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)} ;∅)
Proof step 53:
lpt1[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt2, log, n0) = keyset(gch), n0 < # lpt1, n0 < # lpt2, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1) ⊦ gc-heap(lpt2, log, n0) ∪ (¬ n0 ∈ log ∧ lpt2[n0].flags = LP_GROUP_NODES ⊃ {key-index(lpt2[n0].ref-size, n0)} ;∅) = gc-heap(lpt2, log, n0), lpf = LP_GROUP_NODES ∧ ¬ n0 ∈ log

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: ⊦ n < # lpt1 ∧ id-idx(lpt0, lpt1) → n < # lpt0; (ss) Used terms: n0, log, lpt2