---

Step * of Lemma geo-intersection-unicity

∀e:BasicGeometry. ∀a,b,c,d,p,q:Point.
  ((¬Colinear(a;b;c)) ⇒ c ≠ d ⇒ Colinear(a;b;p) ⇒ Colinear(a;b;q) ⇒ Colinear(c;d;p) ⇒ Colinear(c;d;q) ⇒ p ≡ q)
BY
{ (Auto THEN (gSeparatedCases ⌜p⌝ ⌜q⌝⋅ THEN Auto) THEN Assert ⌜Colinear(a;b;c)⌝⋅ THEN Try (Trivial)) }

1
.....assertion..... 
1. e : BasicGeometry
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. p : Point
7. q : Point
8. ¬Colinear(a;b;c)
9. c ≠ d
10. Colinear(a;b;p)
11. Colinear(a;b;q)
12. Colinear(c;d;p)
13. Colinear(c;d;q)
14. p ≠ q
⊢ Colinear(a;b;c)

---

Latex:

---

Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c,d,p,q:Point.
    ((\mneg{}Colinear(a;b;c))
    {}\mRightarrow{}  c  \mneq{}  d
    {}\mRightarrow{}  Colinear(a;b;p)
    {}\mRightarrow{}  Colinear(a;b;q)
    {}\mRightarrow{}  Colinear(c;d;p)
    {}\mRightarrow{}  Colinear(c;d;q)
    {}\mRightarrow{}  p  \mequiv{}  q)


By

---

Latex:
(Auto  THEN  (gSeparatedCases  \mkleeneopen{}p\mkleeneclose{}  \mkleeneopen{}q\mkleeneclose{}\mcdot{}  THEN  Auto)  THEN  Assert  \mkleeneopen{}Colinear(a;b;c)\mkleeneclose{}\mcdot{}  THEN  Try  (Trivial))

---

Home Index