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BEHBK
PRMBHL
COLMK
NOMEMBHL  defn:parallel
NCMBH  lemma:parallelNC
NCMHL  lemma:parallelNC
NEMB  lemma:NCdistinct
NEHL  lemma:NCdistinct
NCMLH  lemma:NCorder
COMLK  lemma:collinearorder
COHBK  defn:collinear
EQMM  cn:equalityreflexive
EQLL  cn:equalityreflexive
EQBB  cn:equalityreflexive
EQHH  cn:equalityreflexive
EQMK  assumption
 COHBM cn:equalitysub
 COMBH  lemma:collinearorder
 COHLH  defn:collinear
 MEMBHL  defn:meet
NEMK reductio
NCMLH lemma:NCorder
COMLM  defn:collinear
NCMKH  lemma:NChelper
NCHMK  lemma:NCorder
OREQLM|EQLK|EQMK|BEMLK|BELMK|BELKM defn:collinear
cases BELMK:EQLM|EQLK|EQMK|BEMLK|BELMK|BELKM
 case 1:EQLM
  NOBELMK assumption
   COMBM  defn:collinear
   COHLL  defn:collinear
   COHLM  cn:equalitysub
   MEMBHL  defn:meet
  BELMK  reductio
 qedcase
 case 2: EQLK
  NOBELMK assumption
   COHBL  cn:equalitysub
   COHLB  lemma:collinearorder
   COMBB  defn:collinear
   MEMBHL  defn:meet
  BELMK reductio
 qedcase
 case 3: EQMK
  NOBELMK assumption
   NEMK   
  BELMK reductio
 qedcase
 case 4:BEMLK
  NOBELMK assumption
   NCHKM lemma:NCorder
   ANBEHEL+BEMEB  postulate:Pasch-inner
   BEHEL
   BEMEB
   COHEL  defn:collinear
   COMEB  defn:collinear
   COHLE  lemma:collinearorder
   COMBE lemma:collinearorder
   MEMBHL defn:meet
  BELMK reductio
 qedcase
 case 5:BELMK
  BELMK
 qedcase
 case 6:BELKM
  NOBELMK assumption
   NCMLH
   BEMKL  axiom:betweennesssymmetry
   ANBEHEL+BEMBE  postulate:Pasch-outer
   BEHEL
   BEMBE
   COHEL  defn:collinear
   COMBE  defn:collinear
   COHLE  lemma:collinearorder
   MEMBHL defn:meet 
  BELMK reductio
 qedcase
BELMK cases