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Proof step 375 from proof int2bytes-rec-pos-any (previous step)

(8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), # int2bits(j % 2 ^ (i * 8)) / 8 ≤ i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i ⊦ (8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) / 8 = i→n(i) - # int2bits(j % 2 ^ (i * 8)) / 8, i = 0, # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 376:
# int2bits(j % 2 ^ (i * 8)) = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, (8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) % 8 = 0, n = 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m ≤ i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i ⊦ (8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) / 8 = i→n(i) - m, i = 0, # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = []

Rule argument

seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [# int2bits(j % 2 ^ (i * 8)), 8, m, n] rotate: T spec: nat-div inst: name: div-elim

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: # int2bits(j % 2 ^ (i * 8)), 8, m, n