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Proof step 4 from proof bor-bitlength (previous step)

# 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)))) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ # int2bits(bcompl(i)) ≤ # int2bits(i)
Proof step 6:
# 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)))) ⊦

Rule argument

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

Additional information

Used terms: band(bcompl(i), bcompl(j))