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Proof step 6 from proof intshiftrsign32 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, 32 - i→n(band(j, 31)), fillsgn(32, int2bits(i))))

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;%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%mk-len: ⊦ # mklist(boolvar, n) = n; from specification list-last[bitlista]