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Proof step 10 from proof prepost-gcheap-add-log (previous step)

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(nx), ¬ dups(nx0), ¬ 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(lpt[n0].ref-size, 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
lpt[n0] = mklp(m, m0, lpf, m1), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), keyset(gch0) = gc-heap(lpt1, nx), n0 < # lpt, bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[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), dups(nx), dups(nx0), n0 ∈ nx0

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n0], m, m0, lpf, m1]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n0], m, m0, lpf, m1