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Proof step 10 from proof bxor-def-logic (previous step)

⊦ bits2int(bitsxor(int2bits(i), int2bits(j))) = bor(band(i, bits2int(bitsinvert(int2bits(j)))), bits2int(bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)))
Proof step 12:
⊦ bits2int(bitsxor(int2bits(i), int2bits(j))) = bor(bits2int(bitsand(int2bits(i), int2bits(bits2int(bitsinvert(int2bits(j)))))), bits2int(bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j))))

Rule argument

name: band-def rotate: F subst: [j, i] → [bits2int(bitsinvert(int2bits(j))), i]

Additional information

Used terms: bits2int(bitsinvert(int2bits(j))), i