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Proof step 45 from proof prepost-gcheap-add-log (previous step)

# lpt = # lpt1, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m5), lpt[n0] = mklp(m, m0, LP_GROUP_NODES, m1), lpt0[n] = mklp(m2, m3, lpf0, m4), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch1) = (gc-heap(lpt1, nx0) -- key-index(m, n0)) ++ key-index(m, n0), n0 < # lpt1, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), bin-heap-inv(gch1, lpt0), id-idx(lpt, lpt0), ∀ ki. ki ∈ gc-heap(lpt1, nx0) -- key-index(m, n0) → ki.idx ≠ n0, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ (gc-heap(lpt1, nx0) -- key-index(m, n0)) ++ key-index(m, n0) = gc-heap(lpt1, nx0), dups(nx0), dups(nx), n0 ∈ nx0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# lpt = # lpt1, lpt0[n] = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, LP_GROUP_NODES, m1), lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m5), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch1) = gc-heap(lpt1, nx0) ++ key-index(m, n0), n0 < # lpt1, bin-heap-inv(gch1, lpt0), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt, lpt0), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ ki. ki ∈ gc-heap(lpt1, nx0) → ki.idx ≠ n0 ⊦ dups(nx), dups(nx0), n0 ∈ nx0, key-index(m, n0) ∈ gc-heap(lpt1, nx0)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ki ∈ gchs → gchs -- ki = gchs; (s)% ⊦ gchs ++ ki = gchs ↔ ki ∈ gchs; (s)% ⊦ (gchs -- ki) ++ ki = gchs ++ ki; (s)