---

Step * of Lemma real-continuity1

∀a,b:ℝ.
  ∀f:[a, b] ⟶ℝ
    ∀k:ℕ+. ∃d:{d:ℝ| r0 < d} . ∀x,y:{x:ℝ| x ∈ [a, b]} .  ((|x - y| ≤ d) ⇒ (|(f x) - f y| ≤ (r1/r(k)))) 
    supposing ∀x,y:{x:ℝ| x ∈ [a, b]} .  ((x = y) ⇒ ((f x) = (f y))) 
  supposing a ≤ b
BY
{ (Folds ``real-cont real-fun`` 0 THEN InstLemma `real-continuity-ext` [] THEN Trivial) }

---

Latex:

---

Latex:
\mforall{}a,b:\mBbbR{}.
    \mforall{}f:[a,  b]  {}\mrightarrow{}\mBbbR{}
        \mforall{}k:\mBbbN{}\msupplus{}
            \mexists{}d:\{d:\mBbbR{}|  r0  <  d\}  .  \mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  [a,  b]\}  .    ((|x  -  y|  \mleq{}  d)  {}\mRightarrow{}  (|(f  x)  -  f  y|  \mleq{}  (r1/r(k)))) 
        supposing  \mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  [a,  b]\}  .    ((x  =  y)  {}\mRightarrow{}  ((f  x)  =  (f  y))) 
    supposing  a  \mleq{}  b


By

---

Latex:
(Folds  ``real-cont  real-fun``  0  THEN  InstLemma  `real-continuity-ext`  []  THEN  Trivial)

---

Home Index