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Proof step 5 from proof gc-heap-allocate-h (previous step)

lpt[n] = mklp(m0, m1, LP_FREE, m2), n < # lpt, m3 < # lpt, ∀ lpt, n, m0, m1, m2, lp, nx. lpt[n] = mklp(m0, m1, LP_FREE, m2) ∧ n < # lpt ∧ m3 ≤ # lpt → gc-heap(lpt[n, lp], nx + n ', m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, lp], nx + n ', m3 + 1) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpt[m3].flags = LP_GROUP_NODES ⊃ ∅ ++ key-index(lpt[m3].ref-size, m3);∅)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
lpt[n] = mklp(m0, m1, LP_FREE, m2), lpt[m3] = mklp(m, m4, lpf, m5), m3 < # lpt, n < # lpt, ∀ lpt, n, m0, m1, m2, lp, nx. lpt[n] = mklp(m0, m1, LP_FREE, m2) ∧ n < # lpt ∧ m3 ≤ # lpt → gc-heap(lpt[n, lp], nx + n ', m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, lp], nx + n ', m3 + 1) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅)

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[m3], m, m4, lpf, 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: lpt[m3], m, m4, lpf, m5