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Proof step 245 from proof int2bytes-rec-pos-any (previous step)

0 ≤ bytes2int(bits2bytes(int2bits(j % 256))), 0 ≤ j, 0 < j, 256 ≤ j, # int2bits(j % 256) < 8 ⊦ bits2bytes(mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256)) = bits2bytes(int2bits(j % 256)), mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256) = [], 9 = # int2bits(j % 256), # int2bits(j % 256) = 8

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 246:
⊦ # bits ≤ 8 → bits2bytes(bits) = i2b(bits2int(bits)) '
Proof step 247:
# int2bits(j % 256) ≤ 8, 0 ≤ bytes2int(i2b(bits2int(int2bits(j % 256))) '), 0 ≤ j, 0 < j, 256 ≤ j, # int2bits(j % 256) < 8 ⊦ bits2bytes(mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256)) = i2b(bits2int(int2bits(j % 256))) ', mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256) = [], 9 = # int2bits(j % 256), # int2bits(j % 256) = 8

Rule argument

name: bits2bytes-base rotate: F subst: [bits] → [int2bits(j % 256)]

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: int2bits(j % 256)