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Proof step 2 from proof bor-notAndNot (previous step)

⊦ bits2int(bitsor(int2bits(i), 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 3:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsor(bits, bits0) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0)))
Proof step 4:
int2bits(i) ≠ [] ∧ int2bits(j) ≠ [] ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(i)), bitsinvert(int2bits(j))))) = bits2int(bitsinvert(int2bits(bits2int(bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i))))))))

Rule argument

name: or-invandinv rotate: F subst: [bits0, bits] → [int2bits(j), int2bits(i)]

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j), int2bits(i)