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Proof step 19 from proof abs-istore-reduce-write (previous step)

# lpt = # avol, n0 < # avol ∧ lpt[n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore, lpt[n, mklp(m0, m1, lpf, m2)][n0] = mklp(m8, m9, lpf1, m10), istore[n] = indexblock(indx0, lax0, m3), lpt[n] = mklp(m4, m5, lpf0, m6), istore[n, indexblock(indx, lax, m)][n0] = indexblock(indx1, lax1, m7), n < # avol, (lpf0 = LP_INDEX_NODES → abs-leb(avol[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(aleb, indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)), (lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES, n0 ∈ istore → abs-leb(avol[n0], istore[n0], lpt[n0]) ∧ lpt[n0].ref-size = istore[n0].ref-size ⊦ (n0 < # avol ∧ lpf1 = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ (n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol[n, aleb][n0], indexblock(indx1, lax1, m7), mklp(m7, m9, lpf1, m10)) ∧ m8 = m7)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
# lpt = # avol, n0 < # avol ∧ lpt[n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore, istore[n, indexblock(indx, lax, m)][n0] = indexblock(indx1, lax1, m7), lpt[n] = mklp(m4, m5, lpf0, m6), istore[n] = indexblock(indx0, lax0, m3), lpt[n, mklp(m0, m1, lpf, m2)][n0] = mklp(m8, m9, lpf1, m10), istore[n0] = indexblock(indx2, lax2, m11), n < # avol, n0 ∈ istore → abs-leb(avol[n0], istore[n0], lpt[n0]) ∧ lpt[n0].ref-size = m11, (lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES, (lpf0 = LP_INDEX_NODES → abs-leb(avol[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(aleb, indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)) ⊦ (n0 < # avol ∧ lpf1 = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ (n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol[n, aleb][n0], indexblock(indx1, lax1, m7), mklp(m7, m9, lpf1, m10)) ∧ m8 = m7)

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], indx0, lax2, m11]

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], indx0, lax2, m11