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Proof step 55 from proof intshiftrzero-prop-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 56:
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
Proof step 59:
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) ⊦ 32 - i→n(band(j, 31)) = 0, 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

Rule argument

fma: 32 - i→n(band(j, 31)) = 0

Additional information

Used formulas: 32 - i→n(band(j, 31)) = 0