---

Step * of Lemma geo-between_functionality

∀e:EuclideanPlane. ∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1_b1_c1 ⇐⇒ a2_b2_c2))
BY
{ (InstLemma `implies-geo-between_functionality` [] THEN ParallelLast THEN (D -1 THENM Trivial)) }

1
.....antecedent..... 
1. ∀e:EuclideanPlaneStructure
     (BasicGeometryAxioms(e) ⇒ (∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1_b1_c1 ⇐⇒ a2_b2_c2))))
2. e : EuclideanPlane
⊢ BasicGeometryAxioms(e)

---

Latex:

---

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a1,a2,b1,b2,c1,c2:Point.
    (a1  \mequiv{}  a2  {}\mRightarrow{}  b1  \mequiv{}  b2  {}\mRightarrow{}  c1  \mequiv{}  c2  {}\mRightarrow{}  (a1\_b1\_c1  \mLeftarrow{}{}\mRightarrow{}  a2\_b2\_c2))


By

---

Latex:
(InstLemma  `implies-geo-between\_functionality`  []  THEN  ParallelLast  THEN  (D  -1  THENM  Trivial))

---

Home Index