---

Step * of Lemma geo-perp-in-unicity2

∀e:BasicGeometry. ∀a,b,c:Point.
  ((¬Colinear(a;b;c))
  ⇒ (∀d,x:Point.  (c ≠ d ⇒ ab  ⊥x cd ⇒ (∀y:Point. (Colinear(a;b;y) ⇒ Colinear(c;d;y) ⇒ x ≡ y)))))
BY
{ (Auto THEN D -4 THEN InstLemma `geo-intersection-unicity` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜d⌝;⌜x⌝;⌜y⌝]⋅ THEN Auto) }

---

Latex:

---

Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c:Point.
    ((\mneg{}Colinear(a;b;c))
    {}\mRightarrow{}  (\mforall{}d,x:Point.
                (c  \mneq{}  d  {}\mRightarrow{}  ab    \mbot{}x  cd  {}\mRightarrow{}  (\mforall{}y:Point.  (Colinear(a;b;y)  {}\mRightarrow{}  Colinear(c;d;y)  {}\mRightarrow{}  x  \mequiv{}  y)))))


By

---

Latex:
(Auto  THEN  D  -4  THEN  InstLemma  `geo-intersection-unicity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THEN  Auto)

---

Home Index