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Proof step 56 from proof bxor-def-logic (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits)))
Proof step 58:
int2bits(i) ≠ [] ∧ int2bits(j) ≠ [] ⊦ bitsand(bitsinvert(int2bits(i)), int2bits(j)) = [], bitsand(bitsinvert(int2bits(j)), int2bits(i)) = [], bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j)) = [], bits2int(bitsor(bitsand(bitsinvert(int2bits(i)), int2bits(j)), bitsand(bitsinvert(int2bits(j)), int2bits(i)))) = bits2int(bitsor(bitsand(bitsinvert(int2bits(j)), int2bits(i)), bitsand(bitsinvert(int2bits(i)), int2bits(j))))

Rule argument

name: bitsxor-is-orand rotate: F subst: [bits0, bits] → [int2bits(j), int2bits(i)]

Additional information

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