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Proof step 24 from proof bxor-def-logic (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ []

Rule argument

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

Additional information

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