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Proof step 7 from proof exin2pot-neg (previous step)

j + 2 ^ i = 0, 0 ≤ 2 ^ i * 2 + j, 0 < 2 ^ i * 2 + j, 0 ≤ i, j < 0 ⊦ ∃ i. ~1 ≤ i ∧ j + 2 ^ i < 0 ∧ 0 ≤ 2 ^ (i + 1) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i + j = 0 ↔ i = ~ j
Proof step 9:
j = ~(2 ^ i), 0 ≤ 2 ^ i * 2 + j, 0 < 2 ^ i * 2 + j, 0 ≤ i, j < 0 ⊦ ∃ i. ~1 ≤ i ∧ j + 2 ^ i < 0 ∧ 0 ≤ 2 ^ (i + 1) + j

Rule argument

spec: int-abs inst: name: rew-eqzero seq: ⊦ i + j = 0 ↔ i = ~ j subst: [j, i] → [2 ^ i, j] flags: rewrite

Additional information

Used terms: 2 ^ i, j