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Proof step 2 from proof bxor-bitlength (previous step)

# int2bits(i) < n, # int2bits(j) < n, n ≤ # int2bits(bxor(i, j)), # int2bits(i) < # int2bits(bxor(i, j)), # int2bits(j) < # int2bits(bxor(i, j)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bxor(i, j) = bor(band(i, bcompl(j)), band(bcompl(i), j))
Proof step 4:
# 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))) ⊦

Rule argument

name: bxor-def-logic rotate: F subst: [j, i] → [j, i]

Additional information

Used terms: j, i