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

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

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
# int2bits(i) < n, # int2bits(j) < n ⊦ # int2bits(bor(i, j)) < n
Proof step 6:
# int2bits(i) < n, # int2bits(j) < n, n ≤ # int2bits(bor(band(i, bcompl(j)), band(bcompl(i), j))), # int2bits(i) < # int2bits(bor(band(i, bcompl(j)), band(bcompl(i), j))), # int2bits(j) < # int2bits(bor(band(i, bcompl(j)), band(bcompl(i), j))) ⊦ # int2bits(band(i, bcompl(j))) < n ∧ # int2bits(band(bcompl(i), j)) < n

Rule argument

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

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ m ≤ n → (n < m ↔ false); Used terms: band(i, bcompl(j)), n, band(bcompl(i), j)