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Proof step 9 from proof gc-heap-ididx-h (previous step)

lpt1[m0] = mklp(m, m1, lpf, m2), m0 < # lpt1, m0 < # lpt0, id-idx(lpt0, lpt1), ∀ lpt0, lpt1, nx. id-idx(lpt0, lpt1) ∧ m0 ≤ # lpt1 → gc-heap(lpt1, nx, m0) = gc-heap(lpt0, nx, m0) ⊦ gc-heap(lpt1, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅) = gc-heap(lpt0, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpt0[m0].flags = LP_GROUP_NODES ⊃ ∅ ++ key-index(lpt0[m0].ref-size, m0);∅)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
lpt1[m0] = mklp(m, m1, lpf, m2), lpt0[m0] = mklp(m3, m4, lpf0, m5), m0 < # lpt0, m0 < # lpt1, id-idx(lpt0, lpt1), ∀ lpt0, lpt1, nx. id-idx(lpt0, lpt1) ∧ m0 ≤ # lpt1 → gc-heap(lpt1, nx, m0) = gc-heap(lpt0, nx, m0) ⊦ gc-heap(lpt1, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅) = gc-heap(lpt0, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m3, m0);∅)

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[m0], m3, m4, lpf0, m5]

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[m0], m3, m4, lpf0, m5