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Proof step 38 from proof int2bytes-rec-neg-02 (previous step)

i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + int2bits(j % 2 ^ (i * 8)).rest) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)).rest ≠ []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 40:
int2bits(j % 2 ^ (i * 8)) ≠ [], i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + int2bits(j % 2 ^ (i * 8)).rest) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, (# int2bits(j % 2 ^ (i * 8)))-1 % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)).rest ≠ []

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j % 2 ^ (i * 8))] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

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