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Proof step 8 from proof band-bitlength (previous step)

# int2bits(i) ≤ # int2bits(j), n ≤ # bitsand(int2bits(i), int2bits(j)), # int2bits(j) < # sgn(bitsand(int2bits(i), int2bits(j))), # int2bits(i) < # sgn(bitsand(int2bits(i), int2bits(j))), n ≤ # sgn(bitsand(int2bits(i), int2bits(j))), # int2bits(j) < n, # int2bits(i) < n, # int2bits(j) < # bitsand(int2bits(i), int2bits(j)), # int2bits(i) < # bitsand(int2bits(i), int2bits(j)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 10:
int2bits(i) ≠ [] ∧ int2bits(j) ≠ [], # int2bits(i) ≤ # int2bits(j), n ≤ # bitsand(int2bits(j), int2bits(i)), # int2bits(j) < # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(i) < # sgn(bitsand(int2bits(j), int2bits(i))), n ≤ # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(j) < n, # int2bits(i) < n, # int2bits(j) < # bitsand(int2bits(j), int2bits(i)), # int2bits(i) < # bitsand(int2bits(j), int2bits(i)) ⊦

Rule argument

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

Additional information

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