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Proof step 12 from proof abs-gstore-set-lebsize (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
n < # lpt ↔ n ∈ gstore, lpt[n] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore[n] = groupblock(gndx, lax, m), lpt[n, mklp(m3, LEB_SIZE, LP_GROUP_NODES, m5)][n] = mklp(m0, m1, lpf, m2), n < # avol, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], groupblock(gndx, lax, m), mklp(m3, m4, LP_GROUP_NODES, m5)), n ∈ gstore → m3 = m ⊦ (n ∈ gstore → lpf = LP_GROUP_NODES) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∧ (n ∈ gstore → m0 = m)

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)