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Proof step 32 from proof intshiftrzero-prop-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 33:
2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), ~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < band(j, 31) ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = (i i>> j) + 2 * 2 ^ (31 - band(j, 31)), false ∈ int2bits(31).rest
Proof step 73:
~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < band(j, 31) ⊦ 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = (i i>> j) + 2 * 2 ^ (31 - band(j, 31)), false ∈ int2bits(31).rest

Rule argument

fma: 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31))

Additional information

Used formulas: 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31))