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Proof step 7 from proof abs-gstore-reduce-write (previous step)

# lpt = # avol, ∀ n. (n < # avol ∧ 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) ⊦ (∀ n0. (n0 < # avol ∧ 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(avol[n, aleb][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)) ↔ n < # avol ∧ ((lpt[n].flags = LP_GROUP_NODES → lpt[n].ref-size = gstore[n].ref-size) → m0 = m ∧ lpf = LP_GROUP_NODES) ∧ ( ¬ n ∈ ginval ∧ (lpt[n].flags = LP_GROUP_NODES → abs-leb(avol[n], gstore[n], lpt[n])) → abs-leb(aleb, groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
# lpt = # avol, gstore[n] = groupblock(gndx0, lax0, m3), ∀ n. (n < # avol ∧ 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) ⊦ (∀ n0. (n0 < # avol ∧ 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(avol[n, aleb][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)) ↔ n < # avol ∧ ((lpt[n].flags = LP_GROUP_NODES → lpt[n].ref-size = m3) → m0 = m ∧ lpf = LP_GROUP_NODES) ∧ ( ¬ n ∈ ginval ∧ (lpt[n].flags = LP_GROUP_NODES → abs-leb(avol[n], gstore[n], lpt[n])) → abs-leb(aleb, groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)))

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], gndx0, lax0, m3]

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], gndx0, lax0, m3