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Proof step 7 from proof band-bitlength (previous step)

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 cut formula

And obtained the following new goals

Proof step 8:
# 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)) ⊦
Proof step 16:
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)) ⊦ # int2bits(i) ≤ # int2bits(j)

Rule argument

fma: # int2bits(i) ≤ # int2bits(j)

Additional information

Used formulas: # int2bits(i) ≤ # int2bits(j)