---

Step * 1 1 of Lemma ifun-continuous


1. I : Interval
2. icompact(I)
3. f : {f:I ⟶ℝ| ifun(f;I)} 
4. I ~ [left-endpoint(I), right-endpoint(I)]
5. left-endpoint(I) ≤ right-endpoint(I)
⊢ real-cont(λ2x.f[x];left-endpoint(I);right-endpoint(I))
BY
{ (BLemma `real-fun-iff-continuous` THEN Auto THEN (Assert ifun(f;I) BY (DVar `f' THEN Unhide THEN Auto))) }

1
1. I : Interval
2. icompact(I)
3. f : {f:I ⟶ℝ| ifun(f;I)} 
4. I ~ [left-endpoint(I), right-endpoint(I)]
5. left-endpoint(I) ≤ right-endpoint(I)
6. ifun(f;I)
⊢ real-fun(λ2x.f[x];left-endpoint(I);right-endpoint(I))

---

Latex:

---

Latex:

1.  I  :  Interval
2.  icompact(I)
3.  f  :  \{f:I  {}\mrightarrow{}\mBbbR{}|  ifun(f;I)\} 
4.  I  \msim{}  [left-endpoint(I),  right-endpoint(I)]
5.  left-endpoint(I)  \mleq{}  right-endpoint(I)
\mvdash{}  real-cont(\mlambda{}\msubtwo{}x.f[x];left-endpoint(I);right-endpoint(I))


By

---

Latex:
(BLemma  `real-fun-iff-continuous`
  THEN  Auto
  THEN  (Assert  ifun(f;I)  BY
                          (DVar  `f'  THEN  Unhide  THEN  Auto)))

---

Home Index