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Proof step 32 from proof prepost-create-gcheap (previous step)

# lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), bh1 = gch, gc-heap(lpt2, log, n0) = keyset(gch), lpt3 = lpt1, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0 ⊦ ∀ gch, lpt1. bin-heap-inv(gch, lpt1) ∧ id-idx(lpt3, lpt1) ∧ keyset(gch) = keyset(bh1) ++ key-index(m, n0) → ⟪n := n0 + 1⟫ (n ≤ # lpt1 ∧ gc-heap(lpt2, log, n) = keyset(gch) ∧ id-idx(lpt2, lpt1) ∧ # lpt1 < n1 + n), n1 = 0, n0 ∈ log

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, n0) = keyset(gch), keyset(gch0) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n1 ≠ 0, bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt1), id-idx(lpt1, lpt), id-idx(lpt2, lpt1), ¬ n0 ∈ log, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0 ⊦ ⟪n := n0 + 1⟫ (n ≤ # lpt ∧ gc-heap(lpt2, log, n) = keyset(gch0) ∧ # lpt < n1 + n)

Rule argument

Additional information

Used simplifier rules: ⊦ id-idx(lpt0, lpt1) ∧ id-idx(lpt1, lpt2) → id-idx(lpt0, lpt2); (ss)