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Proof step 14 from proof gc-heap-update-h (previous step)

lpt[n] = mklp(m, m4, LP_GROUP_NODES, m5), n < # lpt ⊦ gc-heap(lpt, nx, n) ++ key-index(m6, n) = (gc-heap(lpt, nx, n) -- key-index(m, n)) ++ key-index(m6, n), n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ gchs = gchs0 ++ ki ↔ (∀ ki0. ki0 ∈ gchs ↔ ki0 = ki ∨ ki0 ∈ gchs0)
Proof step 16:
lpt[n] = mklp(m, m4, LP_GROUP_NODES, m5), n < # lpt ⊦ n ∈ nx, ∀ ki0. ki0 ∈ gc-heap(lpt, nx, n) ++ key-index(m6, n) ↔ ki0 = key-index(m6, n) ∨ ki0 ∈ gc-heap(lpt, nx, n) -- key-index(m, n)

Rule argument

spec: set-basic, inst: gc-heap-rename-gc-heap-base-keyindex-set name: ext-rec seq: ⊦ gchs = gchs0 ++ ki ↔ (∀ ki0. ki0 ∈ gchs ↔ ki0 = ki ∨ ki0 ∈ gchs0) subst: [ki, gchs0, gchs] → [key-index(m6, n), gc-heap(lpt, nx, n) -- key-index(m, n), gc-heap(lpt, nx, n) ++ key-index(m6, n)] flags: <all paths>

Additional information

Used terms: key-index(m6, n), gc-heap(lpt, nx, n) -- key-index(m, n), gc-heap(lpt, nx, n) ++ key-index(m6, n)