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Proof step 195 from proof int2bytes-rec-neg-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 196:
⊦ bits ≠ [] → firstn(1, bits) = bits.first '
Proof step 197:
int2bits(j % 2 ^ (i * 8)) ≠ [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), i→n(i) + 1 = # bits2bytes(int2bits(j % 2 ^ (i * 8)).first ') + # bits2bytes(int2bits(j % 2 ^ (i * 8)).rest), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i, 7 < 8 * i→n(i) ⊦ j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0, bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(int2bits(j % 2 ^ (i * 8)).first ') + bits2bytes(int2bits(j % 2 ^ (i * 8)).rest)).rest

Rule argument

seq: ⊦ bits ≠ [] → firstn(1, bits) = bits.first ' subst: [bits] → [int2bits(j % 2 ^ (i * 8))] rotate: F spec: list-del inst: bitlista name: firstN-one

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j % 2 ^ (i * 8))