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Proof step 5 from proof bor-notAndNot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits)
Proof step 7:
¬ bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i)))) ≠ [] ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(i)), bitsinvert(int2bits(j))))) = bits2int(bitsinvert(int2bits(bits2int(bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i))))))))
Proof step 10:
bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i)))) ≠ [] ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(i)), bitsinvert(int2bits(j))))) = bits2int(bitsinvert(sgn(bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i)))))))

Rule argument

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

Additional information

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