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

# int2bits(bcompl(band(bcompl(i), bcompl(j)))) ≤ # int2bits(band(bcompl(i), bcompl(j))), # int2bits(i) < n, # int2bits(j) < n, n ≤ # int2bits(bcompl(band(bcompl(i), bcompl(j)))), # int2bits(i) < # int2bits(bcompl(band(bcompl(i), bcompl(j)))), # int2bits(j) < # int2bits(bcompl(band(bcompl(i), bcompl(j)))), n ≤ # int2bits(band(bcompl(i), bcompl(j))), # int2bits(i) < # int2bits(band(bcompl(i), bcompl(j))), # int2bits(j) < # int2bits(band(bcompl(i), bcompl(j))) ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

name: band-bitlength subst: [i, n, j] → [bcompl(i), n, bcompl(j)]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%bcompl-size-01: ⊦ ¬ # int2bits(i) < # int2bits(bcompl(i));%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ m ≤ n → (n < m ↔ false);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) Used terms: bcompl(i), n, bcompl(j)