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Proof step 111 from proof int2bytes-rec-neg-02 (previous step)

i→n(i) + 1 = # bits2bytes(restn(1, int2bits(j % 2 ^ (i * 8)))) + # bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, 0 < i, 7 < 8 * i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(1, int2bits(j % 2 ^ (i * 8))))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ 0 < n → restn(n, bits) = restn(n -1, bits.rest)
Proof step 113:
0 < 1, i→n(i) + 1 = # bits2bytes(restn(1 -1, int2bits(j % 2 ^ (i * 8)).rest)) + # bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, 0 < i, 7 < 8 * i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(1 -1, int2bits(j % 2 ^ (i * 8)).rest))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0

Rule argument

seq: ⊦ 0 < n → restn(n, bits) = restn(n -1, bits.rest) subst: [bits, n] → [int2bits(j % 2 ^ (i * 8)), 1] rotate: F spec: list-del inst: bitlista name: rest-rec

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: int2bits(j % 2 ^ (i * 8)), 1