---

Step * of Lemma geo-lt-irrefl2

∀e:BasicGeometry. ∀p,q,r:Length.  (p < q + r ⇒ q + r < p ⇒ False)
BY
{ (Auto
   THEN (InstLemma `geo-lt_transitivity`  [⌜e⌝;⌜p⌝;⌜q + r⌝;⌜p⌝]⋅
         THENA (Auto THEN FLemma `geo-le_weakening-lt` [-2] THEN Auto)
         )
   THEN InstLemma `geo-lt-irrefl` [⌜e⌝;⌜p⌝]⋅
   THEN Auto) }

---

Latex:

---

Latex:
\mforall{}e:BasicGeometry.  \mforall{}p,q,r:Length.    (p  <  q  +  r  {}\mRightarrow{}  q  +  r  <  p  {}\mRightarrow{}  False)


By

---

Latex:
(Auto
  THEN  (InstLemma  `geo-lt\_transitivity`    [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{};\mkleeneopen{}q  +  r\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{}]\mcdot{}
              THENA  (Auto  THEN  FLemma  `geo-le\_weakening-lt`  [-2]  THEN  Auto)
              )
  THEN  InstLemma  `geo-lt-irrefl`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{}]\mcdot{}
  THEN  Auto)

---

Home Index