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Proof step 48 from proof abs-gstore-avol-change-other (previous step)

lpt[n3] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[n3] = groupblock(gndx, lax, m), lpt[n] = mklp(n0, n1, lpf, n2), n3 < # lpt, n3 ∈ gstore, n3 ∈ ginval, ∀ 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, n3 = n, (¬ n3 ∈ ginval → abs-leb(avol[n3], groupblock(gndx, lax, m), mklp(m, m1, LP_GROUP_NODES, m2))) ∧ m0 = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
lpt[n3] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[n3] = groupblock(gndx, lax, m), lpt[n] = mklp(n0, n1, lpf, n2), n3 < # lpt, n3 ∈ gstore, n3 ∈ ginval, ∀ 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) ⊦ # ginval = 0, ginval = ∅, lpf = LP_GROUP_NODES, m0 = m, n3 = n

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]