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Proof step 53 from proof bin-heap-inv-write-other (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 54:
key-index(natkey, n) ∈ keyset(kar, m) ↔ key-index(natkey, n) ∈ gc-heap(lpt, nx, # lpt), lpt[n] = mklp(m0, m1, lpf0, m2), kar[m2] = key-index(natkey, n), 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

Rule argument

pos: left 10 terms: key-index(natkey, n) abort: F discard: T computed: F

Additional information

Used terms: key-index(natkey, n)