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Proof step 21 from proof prepost-gcheap-add-log (previous step)

lpt[m2] = mklp(m, m0, lpf, m1), keyset(gch0) = gc-heap(lpt1, nx), m2 < # lpt, bin-heap-inv(bin-heap(kar, m3), lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), key-index(natkey, m2) ∈ keyset(bin-heap(kar, m3)), ∀ n. n = m2 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ ki. ki ∈ keyset(bin-heap(kar, m3)) ↔ ki ∈ gc-heap(lpt1, m2 ' + nx0) ⊦ m3 = 0, dups(nx0), dups(nx), m2 ∈ nx0

User applied rule all left

And obtained the following new goals

Proof step 22:
key-index(natkey, m2) ∈ keyset(bin-heap(kar, m3)) ↔ key-index(natkey, m2) ∈ gc-heap(lpt1, m2 ' + nx0), lpt[m2] = mklp(m, m0, lpf, m1), keyset(gch0) = gc-heap(lpt1, nx), m2 < # lpt, bin-heap-inv(gch0, lpt1), bin-heap-inv(bin-heap(kar, m3), lpt), id-idx(lpt1, lpt), key-index(natkey, m2) ∈ keyset(bin-heap(kar, m3)), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n = m2 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ m3 = 0, dups(nx), dups(nx0), m2 ∈ nx0

Rule argument

pos: left 10 terms: key-index(natkey, m2) abort: F discard: T computed: T

Additional information

Used terms: key-index(natkey, m2)