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Proof step 24 from proof abs-istore-reduce-write-idcircle (previous step)

# lpt = # avol0, # avol1 = # avol0, n0 < # avol0 ∧ 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 < # 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)), n0 ∈ istore → abs-leb(avol0[n0], indexblock(indx2, lax2, lpt[n0].ref-size), lpt[n0]) ∧ lpt[n0].ref-size = m11, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (n0 < # avol0 ∧ lpf1 = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ (n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[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 25:
# avol1 = # avol0, # lpt = # avol0, n0 < # avol0 ∧ lpf2 = LP_INDEX_NODES ↔ n0 ∈ istore, istore[n0] = indexblock(indx2, lax2, m11), 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), lpt[n0] = mklp(m12, m13, lpf2, m14), n < # avol0, n0 ∈ istore → abs-leb(avol0[n0], indexblock(indx2, lax2, m12), lpt[n0]) ∧ m12 = m11, (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] ⊦ (n0 < # avol0 ∧ lpf1 = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ (n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], indexblock(indx1, lax1, m7), mklp(m7, m9, lpf1, m10)) ∧ m8 = m7)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n0], m12, m13, lpf2, m14]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n0], m12, m13, lpf2, m14