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Proof step 22 from proof abs-gstore-reduce-write (previous step)

# lpt = # avol, n0 < # avol ∧ lpt[n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore, gstore[n0] = groupblock(gndx2, lax2, m11), gstore[n] = groupblock(gndx0, lax0, m3), lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n, groupblock(gndx, lax, m)][n0] = groupblock(gndx1, lax1, m7), lpt[n, mklp(m0, m1, lpf, m2)][n0] = mklp(m8, m9, lpf1, m10), n < # avol, ¬ n ∈ ginval ∧ (lpf0 = LP_GROUP_NODES → abs-leb(avol[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, LP_GROUP_NODES, m6))) → abs-leb(aleb, groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)), (lpf0 = LP_GROUP_NODES → m4 = m3) → m0 = m ∧ lpf = LP_GROUP_NODES, n0 ∈ gstore ∧ ¬ n0 ∈ ginval → abs-leb(avol[n0], groupblock(gndx2, lax2, m11), lpt[n0]), n0 ∈ gstore → lpt[n0].ref-size = m11 ⊦ (n0 < # avol ∧ lpf1 = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol[n, aleb][n0], groupblock(gndx1, lax1, m7), mklp(m8, m9, lpf1, m10))) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → m8 = m7)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# lpt = # avol, n0 < # avol ∧ lpf2 = LP_GROUP_NODES ↔ n0 ∈ gstore, lpt[n, mklp(m0, m1, lpf, m2)][n0] = mklp(m8, m9, lpf1, m10), gstore[n, groupblock(gndx, lax, m)][n0] = groupblock(gndx1, lax1, m7), lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n] = groupblock(gndx0, lax0, m3), gstore[n0] = groupblock(gndx2, lax2, m11), lpt[n0] = mklp(m12, m13, lpf2, m14), n < # avol, n0 ∈ gstore → m12 = m11, n0 ∈ gstore ∧ ¬ n0 ∈ ginval → abs-leb(avol[n0], groupblock(gndx2, lax2, m11), lpt[n0]), (lpf0 = LP_GROUP_NODES → m4 = m3) → m0 = m ∧ lpf = LP_GROUP_NODES, ¬ n ∈ ginval ∧ (lpf0 = LP_GROUP_NODES → abs-leb(avol[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, LP_GROUP_NODES, m6))) → abs-leb(aleb, groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)) ⊦ (n0 < # avol ∧ lpf1 = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol[n, aleb][n0], groupblock(gndx1, lax1, m7), mklp(m8, m9, lpf1, m10))) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → m8 = m7)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n0], m12, m13, lpf2, m14]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n0], m12, m13, lpf2, m14