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Proof step 293 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)) = m * 8 + n, i→n(i * 8) % 8 = 0, n < 8, m < i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, m * 8 + n < i→n(i * 8), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ i = 0, m * 8 + n = i→n(i * 8), i→n(i * 8) + 1 = m * 8 + n, mklist(false, 8 * (i→n(i) - 1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - 1 - m = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], n = 0, mklist(i2b(0), i→n(i) - 1 - m) + bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 294:
n < m ⊦ m - 1 - n = m - n + 1
Proof step 295:
m < i→n(i), # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, i→n(i * 8) % 8 = 0, n < 8, m < i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, m * 8 + n < i→n(i * 8), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ i = 0, m * 8 + n = i→n(i * 8), i→n(i * 8) + 1 = m * 8 + n, mklist(false, 8 * (i→n(i) - m + 1)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], n = 0, mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8)))

Rule argument

seq: n < m ⊦ m - 1 - n = m - n + 1 subst: [n, m] → [m, i→n(i)] rotate: F spec: nat inst: name: prop

Additional information

Used terms: m, i→n(i)