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Proof step 32 from proof intshiftrsign32 (previous step)

# mklist(¬ 0 ≤ i, i→n(band(j, 31))) ≤ # int2bits(i), 32 = (n2 + n1) + i→n(band(j, 31)), 32 = n1 + # int2bits(i), # int2bits(i) = i→n(band(j, 31)) + n2, band(j, 31) ≤ 32, # int2bits(i) ≤ 32 ⊦ band(j, 31) = 0, bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, # int2bits(i) - # mklist(¬ 0 ≤ i, i→n(band(j, 31))), int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n2, int2bits(i))), n2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# int2bits(i) = i→n(band(j, 31)) + n2, 32 = n1 + # int2bits(i), 32 = (n2 + n1) + i→n(band(j, 31)), i→n(band(j, 31)) ≤ # int2bits(i), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, # int2bits(i) - i→n(band(j, 31)), int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n2, int2bits(i))), band(j, 31) = 0, n2 = 0

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-ls-zero-01: ⊦ ¬ band(j, 31) < 0;%numleledel: j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); from specification int-abs%num-i2n-le: 0 ≤ i ⊦ i→n(i) ≤ (* m) ↔ i ≤ n→i(m); from specification intnat%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%mk-len: ⊦ # mklist(boolvar, n) = n; from specification list-last[bitlista]