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Proof step 19 from proof band-associativity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits ≠ [] ∧ bits0 ≠ [] → sgn(bitsand(sgn(bits), bits0)) = sgn(bitsand(bits, bits0))
Proof step 21:
bitsand(int2bits(i0), int2bits(j)) ≠ [] ∧ int2bits(i) ≠ [] ⊦ bitsand(sgn(bitsand(int2bits(i), int2bits(i0))), int2bits(j)) = [], sgn(bitsand(bitsand(int2bits(i0), int2bits(j)), int2bits(i))) = sgn(bitsand(bitsand(int2bits(i), int2bits(i0)), int2bits(j)))

Rule argument

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

Additional information

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