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Proof step 56 from proof intshiftrzero-prop-01 (previous step)

32 - i→n(band(j, 31)) = 0, 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), # int2bits(i) ≤ 32, ~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < band(j, 31) ⊦ band(j, 31) = 0, bits2int(mklist(false, i→n(band(j, 31))) + firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))) = 2 ^ (32 - band(j, 31)) + bits2int(mklist(true, i→n(band(j, 31))) + firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))), false ∈ int2bits(31).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), 32 - i→n(band(j, 31)) = 0, 0 < band(j, 31), band(j, 31) ≤ 31, i < 0, ~2147483648 ≤ i, # int2bits(i) ≤ 32 ⊦ band(j, 31) = 0, bits2int(mklist(false, i→n(band(j, 31)))) = bits2int(mklist(true, i→n(band(j, 31)))) + 2 ^ (32 - band(j, 31)), false ∈ int2bits(31).rest

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ firstn(0, bits) = [];