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Proof step 11 from proof band-min-01 (previous step)

band(i, j) < i0, i0 + 2 ^ n→i(# int2bits(i)) ≤ 0, i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, i < 0, j < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)))
Proof step 13:
bits2int(bitsand(int2bits(i), int2bits(j))) < i0, i0 + 2 ^ n→i(# int2bits(i)) ≤ 0, i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, i < 0, j < 0 ⊦

Rule argument

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

Additional information

Used terms: j, i