---

Step * of Lemma arctangent-rminus

∀[x:ℝ]. (arctangent(-(x)) = -(arctangent(x)))
BY
{ (Auto
   THEN InstLemma `arctangent-bounds` [⌜-(x)⌝]⋅
   THEN Auto
   THEN InstLemma `arctangent-bounds` [⌜x⌝]⋅
   THEN Auto
   THEN All Reduce
   THEN BLemma `rtan_one_one`
   THEN Auto) }

1
1. x : ℝ
2. -(π/2) < arctangent(-(x))
3. arctangent(-(x)) < π/2
4. -(π/2) < arctangent(x)
5. arctangent(x) < π/2
⊢ rtan(arctangent(-(x))) = rtan(-(arctangent(x)))

---

Latex:

---

Latex:
\mforall{}[x:\mBbbR{}].  (arctangent(-(x))  =  -(arctangent(x)))


By

---

Latex:
(Auto
  THEN  InstLemma  `arctangent-bounds`  [\mkleeneopen{}-(x)\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  InstLemma  `arctangent-bounds`  [\mkleeneopen{}x\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  All  Reduce
  THEN  BLemma  `rtan\_one\_one`
  THEN  Auto)

---

Home Index