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Proof step 30 from proof prepost-gcheap-add-log (previous step)

lpt[n0] = mklp(m, m0, lpf, m1), keyset(gch1) = keyset(gch) ++ key-index(m, n0), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), n0 < # lpt, bin-heap-inv(gch1, lpt0), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt, lpt0), id-idx(lpt1, lpt), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ ki. ki ∈ keyset(gch) → ki.idx ≠ n0 ⊦ dups(nx), dups(nx0), n0 ∈ nx0, keyset(gch) ++ key-index(m, n0) = gc-heap(lpt1, nx0) ∧ (n ∈ nx0 → n < # lpt0 ∧ lpt0[n].flags = LP_GROUP_NODES)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
lpt[n0] = mklp(m, m0, lpf, m1), lpt0[n] = mklp(m2, m3, lpf0, m4), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), keyset(gch0) = gc-heap(lpt1, nx), keyset(gch1) = keyset(gch) ++ key-index(m, n0), n0 < # lpt, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), bin-heap-inv(gch1, lpt0), id-idx(lpt1, lpt), id-idx(lpt, lpt0), ∀ ki. ki ∈ keyset(gch) → ki.idx ≠ n0, ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ dups(nx0), dups(nx), n0 ∈ nx0, keyset(gch) ++ key-index(m, n0) = gc-heap(lpt1, nx0) ∧ (n ∈ nx0 → n < # lpt0 ∧ lpf0 = LP_GROUP_NODES)

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] → [lpt0[n], m2, m3, lpf0, m4]

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: lpt0[n], m2, m3, lpf0, m4