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Proof step 14 from proof abs-gstore-set-lebsize (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
gstore[n] = groupblock(gndx, lax, m0), lpt[n] = mklp(m0, m4, LP_GROUP_NODES, m2), n < # avol, n < # lpt, abs-leb(avol[n], groupblock(gndx, lax, m0), mklp(m0, m4, LP_GROUP_NODES, m2)), n ∈ gstore ⊦ abs-leb(avol[n], groupblock(gndx, lax, m0), mklp(m0, LEB_SIZE, LP_GROUP_NODES, m2)), n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)