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Proof step 17 from proof abs-gstore-reduce-write-idcircle (previous step)

# lpt = # avol0, # avol1 = # avol0, lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n] = groupblock(gndx0, lax0, m3), n < # avol0, (lpf0 = LP_GROUP_NODES → m4 = m3) → m0 = m ∧ lpf = LP_GROUP_NODES, ¬ n ∈ ginval ∧ (lpf0 = LP_GROUP_NODES → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, LP_GROUP_NODES, m6))) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size), ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ ( n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol1[n0], gstore[n, groupblock(gndx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0])) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = gstore[n, groupblock(gndx, lax, m)][n0].ref-size)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
# avol1 = # avol0, # lpt = # avol0, gstore[n] = groupblock(gndx0, lax0, m3), lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n, groupblock(gndx, lax, m)][n0] = groupblock(gndx1, lax1, m7), n < # avol0, ¬ n ∈ ginval ∧ (lpf0 = LP_GROUP_NODES → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, LP_GROUP_NODES, m6))) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)), (lpf0 = LP_GROUP_NODES → m4 = m3) → m0 = m ∧ lpf = LP_GROUP_NODES, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ ( n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol1[n0], gstore[n, groupblock(gndx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0])) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = m7)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[n, groupblock(gndx, lax, m)][n0], gndx1, lax1, m7]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[n, groupblock(gndx, lax, m)][n0], gndx1, lax1, m7