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Proof step 5 from proof band-bitlength (previous step)

# 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 ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: n ≤ # bitsand(int2bits(i), int2bits(j))

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ # bits < # sgn(bits); Used formulas: n ≤ # bitsand(int2bits(i), int2bits(j))