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Proof step 9 from proof int2bytes-rec-neg-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 11:
¬(# mklist(false, i→n(i * 8)) % 8 = 0 ∧ int2bits(j / 2 ^ (i * 8)) ≠ [] ∧ mklist(false, i→n(i * 8)) ≠ []), j % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8) < 0 ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + mklist(false, i→n(i * 8))) = bits2bytes(int2bits(j / 2 ^ (i * 8))) + fix(i→n(i) + 1, i2b(0) ').rest
Proof step 14:
# mklist(false, i→n(i * 8)) % 8 = 0 ∧ int2bits(j / 2 ^ (i * 8)) ≠ [] ∧ mklist(false, i→n(i * 8)) ≠ [], j % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8) < 0 ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8))) + bits2bytes(mklist(false, i→n(i * 8))) = bits2bytes(int2bits(j / 2 ^ (i * 8))) + fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [mklist(false, i→n(i * 8)), int2bits(j / 2 ^ (i * 8))]

Additional information

Used terms: mklist(false, i→n(i * 8)), int2bits(j / 2 ^ (i * 8))