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Proof step 76 from proof bytes2int-append (previous step)

⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) + 2 ^ (8 * n→i(# bytes0)) * bits2uint(bytes2bits(bytes)) = bits2uint(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1), bytes2bits(bytes).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
0 ≤ i, 0 ≤ j, 0 ≤ j0 ⊦ (i ^ j) ^ j0 = i ^ (j * j0)
Proof step 78:
0 ≤ 2 ∧ 0 ≤ 8 ∧ 0 ≤ n→i(# bytes0) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) + (2 ^ 8) ^ n→i(# bytes0) * bits2uint(bytes2bits(bytes)) = bits2uint(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1), bytes2bits(bytes).first

Rule argument

seq: 0 ≤ i, 0 ≤ j, 0 ≤ j0 ⊦ (i ^ j) ^ j0 = i ^ (j * j0) subst: [j0, j, i] → [n→i(# bytes0), 8, 2] rotate: T spec: int-pot inst: name: pot-pot

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n); Used terms: n→i(# bytes0), 8, 2