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Proof step 15 from proof prepost-create-gcheap (previous step)

# lpt1 = n1 + n0, lpt1[n0].flags = LP_GROUP_NODES, gc-heap(lpt2, log, n0) = keyset(gch), lpt = lpt1, n0 < # lpt1, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), n0 ≤ # lpt1 ⊦ ⟪gc_heap_insert#(key-index(lpt1[n0].ref-size, n0); gch, lpt); n := n0 + 1⟫ (n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt2, log, n) = keyset(gch) ∧ id-idx(lpt2, lpt) ∧ # lpt < n1 + n), n0 ∈ log

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# lpt1 = n1 + n0, lpt1[n0].flags = LP_GROUP_NODES, gc-heap(lpt2, log, n0) = keyset(gch), n1 ≠ 0, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ¬ n0 ∈ log ⊦ ⟪gc_heap_insert#(key-index(lpt1[n0].ref-size, n0); gch, lpt1); n := n0 + 1⟫ (n ≤ # lpt1 ∧ bin-heap-inv(gch, 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% ⊦ m < n → m ≤ n; (s)