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Proof step 36 from proof bxor-def-logic (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bits2int(bitsor(sgn(bits), bits0)) = bits2int(bitsor(bits, bits0))
Proof step 38:
¬(bitsand(bitsinvert(int2bits(j)), int2bits(i)) ≠ [] ∧ sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j))) ≠ []) ⊦ bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j)) = [], bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int(bitsor(sgn(bitsand(bitsinvert(int2bits(j)), int2bits(i))), sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j)))))
Proof step 46:
bitsand(bitsinvert(int2bits(j)), int2bits(i)) ≠ [] ∧ sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j))) ≠ [] ⊦ bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j)) = [], bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int(bitsor(bitsand(bitsinvert(int2bits(j)), int2bits(i)), sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j)))))

Rule argument

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

Additional information

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