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Proof step 3 from proof gc-heap-append-log-h (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ gc-heap(lpt, n ' + nx, m) = gc-heap(lpt, nx, m) -- key-index(n0, n), n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ gchs = gchs0 ↔ (∀ ki. ki ∈ gchs ↔ ki ∈ gchs0)
Proof step 5:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ n ∈ nx, ∀ ki. ki ∈ gc-heap(lpt, n ' + nx, m) ↔ ki ∈ gc-heap(lpt, nx, m) -- key-index(n0, n)

Rule argument

spec: set-basic, inst: gc-heap-rename-gc-heap-base-keyindex-set name: Extension seq: ⊦ gchs = gchs0 ↔ (∀ ki. ki ∈ gchs ↔ ki ∈ gchs0) subst: [gchs0, gchs] → [gc-heap(lpt, nx, m) -- key-index(n0, n), gc-heap(lpt, n ' + nx, m)] flags: <all paths>

Additional information

Used terms: gc-heap(lpt, nx, m) -- key-index(n0, n), gc-heap(lpt, n ' + nx, m)