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Proof step 62 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) ⊦ 32 - i→n(band(j, 31)) = 0, band(j, 31) = 0, bits2uint(firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))) = bits2int(true ' + firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))) + 2 ^ (32 - band(j, 31)), false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ bits.first → bits2uint(bits) = bits2int(bits) + 2 ^ n→i(# bits) subst: [bits] → [firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))] rotate: F spec: int2bits inst: name: ubits2bits

Additional information

Used terms: firstn(32 - i→n(band(j, 31)), fillsgn(32, int2bits(i)))