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Proof step 51 from proof prepost-gcheap-add-log (previous step)

lpt[n].flags = LP_GROUP_NODES, 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, n < # lpt, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), bin-heap-inv(gch1, lpt0), id-idx(lpt1, lpt), id-idx(lpt, lpt0), n ∈ nx0, ∀ ki. ki ∈ keyset(gch) → ki.idx ≠ n0, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ lpf0 = LP_GROUP_NODES, dups(nx0), dups(nx), n0 ∈ nx0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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[n], m5, m6, lpf1, m7]

Additional information

Used simplifier rules: id-idx-fwd-0: ⊦ lpt0[n] = mklp(n0, n1, lpf0, n2) ∧ lpt1[n] = mklp(m0, m1, lpf1, m2) ∧ n < # lpt0 ∧ id-idx(lpt0, lpt1) → n0 = m0 ∧ n1 = m1 ∧ lpf0 = lpf1; (forward) from specification gc-heap-rename%⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n], m5, m6, lpf1, m7