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Proof step 17 from proof negate-01 (previous step)

j < 0, j < 0, j < 0 ⊦ j = 0, rational(i, abs(j)) = ~ rational(~ i, abs(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 0 < j → rational(~ i, j) = ~ rational(i, j)
Proof step 19:
0 < abs(j), j < 0, j < 0, j < 0 ⊦ j = 0, rational(i, abs(j)) = ~ ~ rational(i, abs(j))

Rule argument

name: negate rotate: F subst: [j, i] → [abs(j), i]

Additional information

Used simplifier rules: neg-neg: ⊦ j ≠ 0 → rational(~ i, ~ j) = rational(i, j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: abs(j), i