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Proof step 173 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, 0 < j % 2 ^ (i * 8), 127 < j % 2 ^ (i * 8), # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), # int2bits(j % 2 ^ (i * 8)) ≤ 8, b2i(i2b(j % 2 ^ (i * 8))) < 0 ⊦ mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, # int2bits(j % 2 ^ (i * 8)) % 8 = 0, bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, i2b(j % 2 ^ (i * 8)) ').rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1)) subst: [m, i] → [8, j % 2 ^ (i * 8)] rotate: F spec: int2bits inst: name: int2bits-lelen

Additional information

Used simplifier rules: ⊦ i * j = j * i;%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: 8, j % 2 ^ (i * 8)