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Proof step 9 from proof abs-istore-idcircle (previous step)

# lpt = # avol1, # avol0 = # avol1, lpt[n0] = mklp(m, m3, lpf0, m4), lpt[n] = mklp(m0, m1, lpf, m2), n < # avol1, n0 < # avol1 ∧ n0 ≠ n → avol0[n0] = avol1[n0], ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ lpf = LP_INDEX_NODES, (n0 < # avol1 ∧ lpf0 = LP_INDEX_NODES ↔ n0 ∈ istore) ∧ (n0 ∈ istore → abs-leb(avol1[n0], istore[n0], mklp(istore[n0].ref-size, m3, lpf0, m4)) ∧ m = istore[n0].ref-size)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
# avol0 = # avol1, # lpt = # avol1, lpt[n] = mklp(m0, m1, lpf, m2), lpt[n0] = mklp(m, m3, lpf0, m4), istore[n0] = indexblock(indx, lax, m5), n < # avol1, n0 < # avol1 ∧ n0 ≠ n → avol0[n0] = avol1[n0], ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ lpf = LP_INDEX_NODES, (n0 < # avol1 ∧ lpf0 = LP_INDEX_NODES ↔ n0 ∈ istore) ∧ (n0 ∈ istore → abs-leb(avol1[n0], istore[n0], mklp(m5, m3, lpf0, m4)) ∧ m = m5)

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m) subst: [iblock, indx, lax, m] → [istore[n0], indx, lax, m5]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: istore[n0], indx, lax, m5