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Proof step 42 from proof abs-gstore-avol-change-other (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
lpt[n] = mklp(n0, n1, lpf, n2), gstore[n3] = groupblock(gndx, lax, m), lpt[n3] = mklp(m0, m1, lpf0, m2), n3 < # lpt, ∀ 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, (lpf0 = LP_GROUP_NODES ↔ n3 ∈ gstore) ∧ (n3 ∈ gstore ∧ ¬ n3 ∈ ginval → abs-leb(avol[n3], groupblock(gndx, lax, m), mklp(m0, m1, lpf0, m2))) ∧ (n3 ∈ gstore → m0 = m)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic