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Proof step 14 from proof prepost-create-gcheap (previous step)

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 ∈ log ⊦ ⟪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 < (# lpt1 - n0) + n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
# 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

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# lpt1, n0, n1]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # lpt1, n0, n1