---

Step * of Lemma partition-choice-member

∀I:Interval
  (icompact(I)
  ⇒ (∀p:partition(I). ∀x:partition-choice(full-partition(I;p)). ∀i:ℕ||full-partition(I;p)|| - 1.  (x i ∈ {x:ℝ| x ∈ I} )\000C))
BY
{ (Auto
   THEN MemTypeCD
   THEN Auto
   THEN Try ((RepUR ``full-partition`` 0 THEN Auto'))
   THEN Unfold `partition-choice` (-2)
   THEN GenConclAtAddr [2]⋅
   THEN Auto
   THEN Try ((RepUR ``full-partition`` 0 THEN Auto'))) }

1
1. I : Interval@i
2. icompact(I)@i
3. p : partition(I)@i
4. x : i:ℕ||full-partition(I;p)|| - 1 ⟶ {x:ℝ| x ∈ [full-partition(I;p)[i], full-partition(I;p)[i + 1]]} @i
5. i : ℕ||full-partition(I;p)|| - 1@i
6. v : {x:ℝ| x ∈ [full-partition(I;p)[i], full-partition(I;p)[i + 1]]} @i
7. (x i) = v ∈ {x:ℝ| x ∈ [full-partition(I;p)[i], full-partition(I;p)[i + 1]]} @i
⊢ v ∈ I

---

Latex:

---

Latex:
\mforall{}I:Interval
    (icompact(I)
    {}\mRightarrow{}  (\mforall{}p:partition(I).  \mforall{}x:partition-choice(full-partition(I;p)).  \mforall{}i:\mBbbN{}||full-partition(I;p)||  -  1.
                (x  i  \mmember{}  \{x:\mBbbR{}|  x  \mmember{}  I\}  )))


By

---

Latex:
(Auto
  THEN  MemTypeCD
  THEN  Auto
  THEN  Try  ((RepUR  ``full-partition``  0  THEN  Auto'))
  THEN  Unfold  `partition-choice`  (-2)
  THEN  GenConclAtAddr  [2]\mcdot{}
  THEN  Auto
  THEN  Try  ((RepUR  ``full-partition``  0  THEN  Auto')))

---

Home Index