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Proof step 10 from proof band-associativity (previous step)

bitsand(sgn(bitsand(int2bits(i), int2bits(i0))), int2bits(j)) = [] ⊦ bits2int(bitsand(int2bits(i), sgn(bitsand(int2bits(i0), int2bits(j))))) = bits2int([])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ []

Rule argument

name: and-notempty rotate: F subst: [bits0, bits] → [int2bits(j), sgn(bitsand(int2bits(i), int2bits(i0)))]

Additional information

Used simplifier rules: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ [];% ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j), sgn(bitsand(int2bits(i), int2bits(i0)))