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Proof step 15 from proof bxor-def-logic (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits)
Proof step 17:
¬ bitsand(int2bits(i), sgn(bitsinvert(int2bits(j)))) ≠ [] ⊦ bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int (bitsor (int2bits(bits2int(bitsand(int2bits(i), sgn(bitsinvert(int2bits(j)))))), int2bits(bits2int(bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j))))))
Proof step 20:
bitsand(int2bits(i), sgn(bitsinvert(int2bits(j)))) ≠ [] ⊦ bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int(bitsor(sgn(bitsand(int2bits(i), sgn(bitsinvert(int2bits(j))))), int2bits(bits2int(bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j))))))

Rule argument

seq: bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits) subst: [bits] → [bitsand(int2bits(i), sgn(bitsinvert(int2bits(j))))] rotate: F spec: int2bits inst: name: bits2bits-def

Additional information

Used terms: bitsand(int2bits(i), sgn(bitsinvert(int2bits(j))))