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Proof step 170 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 171:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 172:
¬(~128 ≤ j % 2 ^ (i * 8) ∧ j % 2 ^ (i * 8) ≤ 127), i→n(i * 8) % 8 = 0, b2i(i2b(j % 2 ^ (i * 8))) < 0, # int2bits(j % 2 ^ (i * 8)) ≤ 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8) ⊦ 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, # int2bits(j % 2 ^ (i * 8)) % 8 = 0, i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = []

Rule argument

seq: ~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i subst: [i] → [j % 2 ^ (i * 8)] rotate: F spec: byte inst: name: num-ibbi

Additional information

Used simplifier rules: ⊦ i * j = j * i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j % 2 ^ (i * 8)