Nuprl Lemma : symmetry-preserves-congruence
∀e:BasicGeometry. ∀A,P,Q,p,q:Point.  (p=A=P 
⇒ q=A=Q 
⇒ PQ ≅ pq)
Proof
Definitions occuring in Statement : 
basic-geometry: BasicGeometry
, 
geo-midpoint: a=m=b
, 
geo-congruent: ab ≅ cd
, 
geo-point: Point
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Lemmas referenced : 
geo-midpoint-diagonals-congruent
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
hypothesis
Latex:
\mforall{}e:BasicGeometry.  \mforall{}A,P,Q,p,q:Point.    (p=A=P  {}\mRightarrow{}  q=A=Q  {}\mRightarrow{}  PQ  \mcong{}  pq)
Date html generated:
2019_10_16-PM-01_28_19
Last ObjectModification:
2019_08_26-PM-09_12_10
Theory : euclidean!plane!geometry
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