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Proof step 83 from proof bytes2int-append (previous step)

0 ≤ 2 ∧ 0 ≤ 8 ∧ 0 ≤ n→i(# bytes0) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = band(bits2int(bytes2bits(bytes0)), 2 ^ (8 * n→i(# bytes0)) - 1), bytes2bits(bytes).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 84:
⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i
Proof step 85:
¬(0 ≤ bits2int(bytes2bits(bytes0)) ∧ 0 ≤ 8 * n→i(# bytes0)), 0 ≤ 2 ∧ 0 ≤ 8 ∧ 0 ≤ n→i(# bytes0) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = band(bits2int(bytes2bits(bytes0)), 2 ^ (8 * n→i(# bytes0)) - 1), bytes2bits(bytes).first
Proof step 103:
0 ≤ bits2int(bytes2bits(bytes0)) ∧ 0 ≤ 8 * n→i(# bytes0), 0 ≤ 2 ∧ 0 ≤ 8 ∧ 0 ≤ n→i(# bytes0) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = bits2int(bytes2bits(bytes0)) % 2 ^ (8 * n→i(# bytes0)), bytes2bits(bytes).first

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i subst: [i, j] → [8 * n→i(# bytes0), bits2int(bytes2bits(bytes0))] rotate: F spec: intops inst: name: band-011x-pos

Additional information

Used terms: 8 * n→i(# bytes0), bits2int(bytes2bits(bytes0))