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Proof step 28 from proof abs-istore-reduce-write-idcircle (previous step)

# 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), n0 = n, n < # avol0, n0 < # avol0 ∧ n0 ≠ n → avol1[n0] = avol0[n0], (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, n0 ∈ istore → abs-leb(avol0[n0], indexblock(indx2, lax2, m11), mklp(m11, m13, lpf2, m14)) ∧ m12 = m11 ⊦ (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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# lpt = # avol0, # avol1 = # avol0, lpf2 = LP_INDEX_NODES ↔ n ∈ istore, lpt[n] = mklp(m12, m13, lpf2, m14), istore[n] = indexblock(indx0, lax0, m3), n < # avol0, n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m3, m13, lpf2, m14)) ∧ m12 = m3, (n ∈ istore → m12 = m3) → m8 = m7 ∧ lpf1 = LP_INDEX_NODES, (n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m12, m13, LP_INDEX_NODES, m14))) → abs-leb(avol1[n], indexblock(indx1, lax1, m7), mklp(m8, m9, lpf1, m10)) ⊦ lpf1 = LP_INDEX_NODES ∧ abs-leb(avol1[n], indexblock(indx1, lax1, m7), mklp(m7, m9, LP_INDEX_NODES, m10)) ∧ m8 = m7

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ istore[n, iblock]; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%⊦ indexblock(indx, lax, m) = indexblock(indx0, lax0, m0) ↔ indx = indx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ istore[n, iblock][n] = iblock; (s)