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Proof step 3 from proof abs-gstore-lpt-change-other (previous step)

lpt[n] = mklp(n0, n1, lpf, n2) ⊦ lp.flags = LP_GROUP_NODES, (∀ n3. (n3 < # lpt ∧ lpt[n, lp][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)) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size)), lpf = LP_GROUP_NODES

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
lpt[n] = mklp(n0, n1, lpf, n2), lp = mklp(m, m0, lpf0, m1) ⊦ (∀ n3. (n3 < # lpt ∧ lpt[n, lp][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)) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size)), lpf = LP_GROUP_NODES, 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] → [lp, m, m0, lpf0]

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: lp, m, m0, lpf0