---

Step * 1 1 of Lemma Euclid-Prop19-weak


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. a # bc
6. bca < abc
7. |ac| < |ab|
8. abc < bca
⊢ ¬¬|ab| < |ac|
BY
{ ((InstLemma `geo-lt-angle-trans` [⌜e⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜b⌝;⌜c⌝;⌜a⌝]⋅ THENA Auto)
   THEN InstLemma `lt-angle-not-cong` [⌜e⌝]⋅
   THEN Auto) }

---

Latex:

---

Latex:

1.  e  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  a  \#  bc
6.  bca  <  abc
7.  |ac|  <  |ab|
8.  abc  <  bca
\mvdash{}  \mneg{}\mneg{}|ab|  <  |ac|


By

---

Latex:
((InstLemma  `geo-lt-angle-trans`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  InstLemma  `lt-angle-not-cong`  [\mkleeneopen{}e\mkleeneclose{}]\mcdot{}
  THEN  Auto)

---

Home Index