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Proof step 17 from proof int2bits-rec-neg (previous step)

(j - 1) / 2 < 0, j ≤ 0, j < 0 ⊦ 0 = j % 2, sgn((bitsinvert(uint2bits(~(j / 2))) + (~1 ≠ j % 2)')+1) = sgn(bitsinvert(uint2bits((1 - j) / 2)) +1) + (~1 = j % 2)', ~1 = j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
j = i * 2 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ∧ 0 < 2, (j - 1) / 2 < 0, j ≤ 0, j < 0 ⊦ 0 = j0, sgn((bitsinvert(uint2bits(~ i)) + (~1 ≠ j0)')+1) = sgn(bitsinvert(uint2bits((1 - j) / 2)) +1) + (~1 = j0)', ~1 = j

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j) subst: [i, j, i0, j0] → [j, 2, i, j0] rotate: T spec: int-div inst: name: div-elim2

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward)%⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j); (elim) Used terms: j, 2, i, j0