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:  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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