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Proof step 21 from proof prepost-create-gcheap (previous step)

# lpt1 = n1 + ki.idx, lpt1[ki.idx] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, ki.idx) = keyset(gch), bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ki ∈ keyset(gch) ⊦ # keyset(gch) = 0, gch.size = 0, n1 = 0, ki.idx ∈ log

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# lpt1 = n1 + m2, lpt1[m2] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, m2) = keyset(gch), ki = key-index(natkey, m2), bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ki ∈ keyset(gch) ⊦ # keyset(gch) = 0, gch.size = 0, n1 = 0, m2 ∈ log

Rule argument

spec: key-index, inst: gc-heap-rename-gc-heap-base name: elim seq: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m) subst: [ki, n, n0] → [ki, n0, n5]

Additional information

Used simplifier rules: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m); (elim) Used terms: ki, n0, n5