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Proof step 29 from proof abs-gstore-lpt-change-other (previous step)

lpt[n3] = mklp(m3, m4, LP_GROUP_NODES, m5), lpt[n] = mklp(n0, n1, lpf, n2), (∅)[n3] = groupblock(gndx, lax, m2), n3 < # lpt, ∀ n3. (n3 < # lpt ∧ lpt[n, mklp(m, m0, lpf0, m1)][n3].flags = LP_GROUP_NODES ↔ n3 ∈ gstore) ∧ (n3 ∈ gstore ∧ ¬ n3 ∈ ginval → abs-leb(avol[n3], gstore[n3], lpt[n3])) ∧ (n3 ∈ gstore → lpt[n3].ref-size = gstore[n3].ref-size) ⊦ lpt[n, mklp(m, m0, lpf0, m1)][n3].flags = LP_GROUP_NODES, lpf = LP_GROUP_NODES, lpf0 = LP_GROUP_NODES, n3 ∈ gstore

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
(∅)[n3] = groupblock(gndx, lax, m2), lpt[n] = mklp(n0, n1, lpf, n2), lpt[n3] = mklp(m3, m4, LP_GROUP_NODES, m5), lpt[n, mklp(m, m0, lpf0, m1)][n3] = mklp(m6, m7, lpf1, m8), n3 < # lpt, ∀ n3. (n3 < # lpt ∧ lpt[n, mklp(m, m0, lpf0, m1)][n3].flags = LP_GROUP_NODES ↔ n3 ∈ gstore) ∧ (n3 ∈ gstore ∧ ¬ n3 ∈ ginval → abs-leb(avol[n3], gstore[n3], lpt[n3])) ∧ (n3 ∈ gstore → lpt[n3].ref-size = gstore[n3].ref-size) ⊦ lpf = LP_GROUP_NODES, lpf0 = LP_GROUP_NODES, lpf1 = LP_GROUP_NODES, n3 ∈ gstore

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, mklp(m, m0, lpf0, m1)][n3], m6, m7, lpf1, m8]

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[n, mklp(m, m0, lpf0, m1)][n3], m6, m7, lpf1, m8