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Proof step 116 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 117:
n ≤ m ⊦ (m - n) + n = m
Proof step 118:
# int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), i→n(i * 8) % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), 0 ≤ j % 2 ^ (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)) = [], bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

seq: n ≤ m ⊦ (m - n) + n = m subst: [n, m] → [# int2bits(j % 2 ^ (i * 8)), i→n(i * 8)] rotate: F spec: nat inst: name: prop-01

Additional information

Used simplifier rules: ⊦ m + n = n + m; Used terms: # int2bits(j % 2 ^ (i * 8)), i→n(i * 8)