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Proof step 17 from proof bor-notAndNot (previous step)

⊦ 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(i))), bitsinvert(int2bits(j))))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ bits ≠ [] ∧ bits0 ≠ [] → sgn(bitsand(sgn(bits), bits0)) = sgn(bitsand(bits, bits0))
Proof step 19:
bitsinvert(int2bits(i)) ≠ [] ∧ bitsinvert(int2bits(j)) ≠ [] ⊦ bitsand(sgn(bitsinvert(int2bits(j))), sgn(bitsinvert(int2bits(i)))) = [], bits2int(bitsinvert(bitsand(bitsinvert(int2bits(i)), bitsinvert(int2bits(j))))) = bits2int(bitsinvert(sgn(bitsand(bitsinvert(int2bits(i)), bitsinvert(int2bits(j))))))

Rule argument

name: and-sgn rotate: F subst: [bits0, bits] → [bitsinvert(int2bits(j)), bitsinvert(int2bits(i))]

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: bitsinvert(int2bits(j)), bitsinvert(int2bits(i))