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Proof step 12 from proof prepost-gcheap-add-log (previous step)

lpt[n0] = mklp(m, m0, lpf, m1), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), n0 < # lpt, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), id-idx(lpt1, lpt), ¬ dups(nx0), ¬ dups(nx), ¬ n0 ∈ nx0, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ ⟪gc_heap_insert#(key-index(m, n0); gch, lpt); log := nx0⟫ ( bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt1, log) ∧ id-idx(lpt1, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES) ∧ ¬ # nx0 < # log)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: prepost-insert seq: bin-heap-inv(bh, lpt), lpt0 = lpt, bh0 = bh, ki.idx < # lpt, ∀ ki0. ki0 ∈ keyset(bh0) → ki0.idx ≠ ki.idx ⊦ ⟪gc_heap_insert#(ki; bh, lpt)⟫ ( bin-heap-inv(bh, lpt) ∧ id-idx(lpt0, lpt) ∧ keyset(bh) = keyset(bh0) ++ ki) subst: [ki, lpt, bh, lpt0, bh0] → [key-index(m, n0), lpt, gch, lpt, gch] flags: <all paths>

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