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

# lpt = # avol0, # avol1 = # avol0, lpt[n] = mklp(m4, m5, lpf0, m6), istore[n] = indexblock(indx0, lax0, m3), n < # avol0, (lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES, (lpf0 = LP_INDEX_NODES → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)), ∀ n. (n < # avol0 ∧ 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), ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0]) ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = istore[n, indexblock(indx, 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, 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 < # avol0, (lpf0 = LP_INDEX_NODES → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)), (lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n. (n < # avol0 ∧ 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) ⊦ (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0]) ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = 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[n, indexblock(indx, lax, m)][n0], indx1, lax1, m7]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: istore[n, indexblock(indx, lax, m)][n0], indx1, lax1, m7