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Proof step 51 from proof bin-heap-inv-write-other (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), kar[m2] = key-index(natkey, n), keyset(kar, m) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), m2 < m, n < # lpt, m2 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf0 = LP_GROUP_NODES, m6 = m2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ gchs = gchs0 ↔ (∀ ki. ki ∈ gchs ↔ ki ∈ gchs0)
Proof step 53:
kar[m2] = key-index(natkey, n), lpt[n] = mklp(m0, m1, lpf0, m2), 2exp-size(# kar), m2 < # kar, n < # lpt, m2 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ ki. ki ∈ keyset(kar, m) ↔ ki ∈ gc-heap(lpt, nx, # lpt) ⊦ lpf0 = LP_GROUP_NODES, m6 = m2

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, # lpt), keyset(kar, m)] flags: <all paths>

Additional information

Used terms: gc-heap(lpt, nx, # lpt), keyset(kar, m)