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Proof step 13 from proof int2bytes-rec-neg-04 (previous step)

0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ bits2bytes(int2bits(j0) + mklist(false, i→n(i * 8))) = int2bytes(j0) + fix(i→n(i) + 1, i2b(0) ').rest, j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 15:
¬(# mklist(false, i→n(i * 8)) % 8 = 0 ∧ int2bits(j0) ≠ [] ∧ mklist(false, i→n(i * 8)) ≠ []), 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ bits2bytes(int2bits(j0) + mklist(false, i→n(i * 8))) = int2bytes(j0) + fix(i→n(i) + 1, i2b(0) ').rest, j0 = 0
Proof step 18:
# mklist(false, i→n(i * 8)) % 8 = 0 ∧ int2bits(j0) ≠ [] ∧ mklist(false, i→n(i * 8)) ≠ [], 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ bits2bytes(int2bits(j0)) + bits2bytes(mklist(false, i→n(i * 8))) = int2bytes(j0) + fix(i→n(i) + 1, i2b(0) ').rest, j0 = 0

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [mklist(false, i→n(i * 8)), int2bits(j0)]

Additional information

Used terms: mklist(false, i→n(i * 8)), int2bits(j0)