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Proof step 13 from proof band-bitlength (previous step)

¬(¬ int2bits(i).first ∧ # int2bits(i) ≤ # int2bits(j) ∧ int2bits(i) ≠ []), # int2bits(i) < # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(i) < # bitsand(int2bits(j), int2bits(i)), # int2bits(j) < # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(j) < # bitsand(int2bits(j), int2bits(i)), # int2bits(i) < n, # int2bits(j) < n, n ≤ # sgn(bitsand(int2bits(j), int2bits(i))), n ≤ # bitsand(int2bits(j), int2bits(i)), # int2bits(i) ≤ # int2bits(j) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# int2bits(i) < # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(i) < # bitsand(int2bits(j), int2bits(i)), # int2bits(j) < # sgn(bitsand(int2bits(j), int2bits(i))), # int2bits(j) < # bitsand(int2bits(j), int2bits(i)), # int2bits(i) < n, # int2bits(j) < n, n ≤ # sgn(bitsand(int2bits(j), int2bits(i))), n ≤ # bitsand(int2bits(j), int2bits(i)), # int2bits(i) ≤ # int2bits(j), i < 0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ m ≤ n → (n < m ↔ false);% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ int2bits(j).first ↔ j < 0;