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Proof step 18 from proof abs-gstore-lpt-change-other (previous step)

lpt[n3] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore[n3] = groupblock(gndx, lax, m2), lpt[n] = mklp(n0, n1, lpf, n2), n3 < # lpt, n3 ∈ gstore, n3 ∈ ginval, ∀ 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, (¬ n3 ∈ ginval → abs-leb(avol[n3], groupblock(gndx, lax, m2), mklp(m2, m4, LP_GROUP_NODES, m5))) ∧ m3 = m2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
lpt[n3] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore[n3] = groupblock(gndx, lax, m2), lpt[n] = mklp(n0, n1, lpf, n2), n3 < # lpt, n3 ∈ gstore, n3 ∈ ginval, ∀ 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) ⊦ # ginval = 0, ginval = ∅, lpf = LP_GROUP_NODES, lpf0 = LP_GROUP_NODES, m3 = m2

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]