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Proof step 25 from proof prepost-create-gcheap (previous step)

# lpt1 = n1 + m2, lpt1[m2] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, m2) = keyset(bin-heap(kar, m3)), bin-heap-inv(bin-heap(kar, m3), lpt1), id-idx(lpt2, lpt1), key-index(natkey, m2) ∈ gc-heap(lpt2, log, m2) ⊦ # gc-heap(lpt2, log, m2) = 0, gc-heap(lpt2, log, m2) = ∅, m3 = 0, n1 = 0, m2 ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES)
Proof step 27:
# lpt1 = n1 + m2, lpt1[m2] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, m2) = keyset(bin-heap(kar, m3)), bin-heap-inv(bin-heap(kar, m3), lpt1), id-idx(lpt2, lpt1), key-index(natkey, m2) ∈ gc-heap(lpt2, log, m2) ⊦ # gc-heap(lpt2, log, m2) = 0, gc-heap(lpt2, log, m2) = ∅, m3 = 0, n1 = 0, m2 ∈ log, m2 ≤ # lpt2

Rule argument

spec: persistence-base name: gc-heap-in-h seq: ⊦ n ≤ # lpt → ( key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES) subst: [n, nx, lpt, n1, n0] → [m2, log, lpt2, m2, natkey] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s) Used terms: m2, log, lpt2, m2, natkey