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Proof step 20 from proof prepost-create-gcheap (previous step)

# lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, n0) = keyset(gch), bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1) ⊦ n1 = 0, n0 ∈ log, bin-heap-inv(gch, lpt1) ∧ lpt1 = lpt1 ∧ gch = gch ∧ key-index(m, n0).idx < # lpt1 ∧ (∀ ki0. ki0 ∈ keyset(gch) → ki0.idx ≠ key-index(m, n0).idx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# 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

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);% ⊦ bin-heap-inv(bh, lpt) → (keyset(bh) = ∅ ↔ bh.size = 0); (s)%size-zero-01: ⊦ gchs ≠ ∅ → # gchs ≠ 0; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%ne-01: ⊦ ki ∈ gchs → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ key-index(natkey, m).idx = m; (s)