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Proof step 30 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), gch = gch, ki0 = key-index(m, n0), lpt1 = lpt1, lpt3 = lpt1, key-index(m, n0).idx < # lpt1, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ∀ ki0. ki0 ∈ keyset(gch) → ki0.idx ≠ key-index(m, n0).idx ⊦ [gc_heap_insert#(key-index(m, n0); gch, lpt1)] ( bin-heap-inv(gch, lpt1) ∧ id-idx(lpt3, lpt1) ∧ keyset(gch) = keyset(bh1) ++ ki0 → ⟪n := n0 + 1⟫ (n ≤ # lpt1 ∧ bin-heap-inv(gch, 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 31:
# lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), bh1 = gch, gc-heap(lpt2, log, n0) = keyset(gch), lpt3 = lpt1, n1 ≠ 0, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ¬ n0 ∈ log, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0 ⊦ [gc_heap_insert#(key-index(m, 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))

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);%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)