---

Step * 1 of Lemma mesh-uniform-partition


1. I : Interval
2. icompact(I)
3. k : ℕ+
4. 2 ≤ ||full-partition(I;uniform-partition(I;k))||
5. i : ℕ(||full-partition(I;uniform-partition(I;k))|| - 2) + 1
6. ||full-partition(I;uniform-partition(I;k))|| = (k + 1) ∈ ℤ
7. i < k
⊢ ((r(k) * full-partition(I;uniform-partition(I;k))[i + 1]) + -(r(k) * full-partition(I;uniform-partition(I;k))[i]))
= |I|
BY
{ ((RWO "rmul_comm" 0⋅ THENA Auto) THEN RWO "uniform-partition-point" 0 THEN Auto) }

1
1. I : Interval
2. icompact(I)
3. k : ℕ+
4. 2 ≤ ||full-partition(I;uniform-partition(I;k))||
5. i : ℕ(||full-partition(I;uniform-partition(I;k))|| - 2) + 1
6. ||full-partition(I;uniform-partition(I;k))|| = (k + 1) ∈ ℤ
7. i < k
⊢ ((((r(k) - r(i + 1)) * left-endpoint(I)) + (r(i + 1) * right-endpoint(I)))
+ -(((r(k) - r(i)) * left-endpoint(I)) + (r(i) * right-endpoint(I))))
= |I|

---

Latex:

---

Latex:

1.  I  :  Interval
2.  icompact(I)
3.  k  :  \mBbbN{}\msupplus{}
4.  2  \mleq{}  ||full-partition(I;uniform-partition(I;k))||
5.  i  :  \mBbbN{}(||full-partition(I;uniform-partition(I;k))||  -  2)  +  1
6.  ||full-partition(I;uniform-partition(I;k))||  =  (k  +  1)
7.  i  <  k
\mvdash{}  ((r(k)  *  full-partition(I;uniform-partition(I;k))[i  +  1])
+  -(r(k)  *  full-partition(I;uniform-partition(I;k))[i]))
=  |I|


By

---

Latex:
((RWO  "rmul\_comm"  0\mcdot{}  THENA  Auto)  THEN  RWO  "uniform-partition-point"  0  THEN  Auto)

---

Home Index