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Proof step 4 from proof int2bits-mod2-neg (previous step)

abs(j) < 2, j ≤ 0, i0 ≤ 0, i0 * 2 + j < 0 ⊦ int2bits(j) = int2bits(i0 * 2 + j).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Proof step 6:
¬(i0 * 2 + j < 0 ∧ i0 * 2 + j ≠ ~1), abs(j) < 2, j ≤ 0, i0 ≤ 0, i0 * 2 + j < 0 ⊦ int2bits(j) = int2bits(i0 * 2 + j).last '
Proof step 9:
i0 * 2 + j < 0 ∧ i0 * 2 + j ≠ ~1, abs(j) < 2, j ≤ 0, i0 ≤ 0, i0 * 2 + j < 0 ⊦ int2bits(j) = (int2bits((i0 * 2 + j - 1) / 2) + (~1 = (i0 * 2 + j) % 2)').last '

Rule argument

name: int2bits-rec-neg rotate: F subst: [j] → [i0 * 2 + j]

Additional information

Used terms: i0 * 2 + j