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TRABC
TRDEF
EEABDE
EEACDF
AOEDFBAC
NCABC  defn:triangle
EQAB assumption
 COABC  defn:collinear
NEAB  reductio
EQAC  assumption
 COABC  defn:collinear
NEAC  reductio
NECA  lemma:inequalitysymmetric
EQBC assumption
 COABC defn:collinear
NEBC  reductio
NECB  lemma:inequalitysymmetric
ANBEPTQ+RAABP+RAACQ+EAEDFBAT defn:anglelessthan
RAABP
RAACQ
EAEDFBAT
NCBAT   lemma:equalanglesNC
EQAT  assumption
 COBAT  defn:collinear
NEAT  reductio
EQAC  assumption
 COABC defn:collinear
NEAC reductio
ANRAATH+EEAHAC  lemma:layoff
RAATH
EEAHAC
EEACDF
EEAHDF  lemma:congruencetransitive
COHAB  assumption
 COATH  lemma:rayimpliescollinear
 COHAT lemma:collinearorder
 NEAH  lemma:raystrict
 NEHA  lemma:inequalitysymmetric
 COABT lemma:collinear4
 COBAT lemma:collinearorder
NCHAB  reductio
EQHB assumption
 COHAB  defn:collinear
NEHB reductio
EEABDE
EAEDFBAT
RAATH  
EQBB    cn:equalityreflexive  
RAABB   lemma:ray4
EAEDFBAH  lemma:equalangleshelper
EABAHEDF  lemma:equalanglessymmetric
EAHABFDE  lemma:equalanglesflip
ANEEHBFE+EAAHBDFE+EAABHDEF  proposition:04
RAAQC   lemma:ray5
RAAPB   lemma:ray5
COAQC  lemma:rayimpliescollinear
COAPB  lemma:rayimpliescollinear
COQAP   assumption
 COAPQ  lemma:collinearorder
 COQAC  lemma:collinearorder
 COQAP  lemma:collinearorder
 NEAQ  lemma:ray2
 NEQA  lemma:inequalitysymmetric
 COACP  lemma:collinear4
 COPAB  lemma:collinearorder
 COPAC  lemma:collinearorder
 NEAP  lemma:raystrict
 NEPA  lemma:inequalitysymmetric
 COABC lemma:collinear4
NCQAP   reductio
TRQAP  defn:triangle
BEPTQ
BEQTP  axiom:betweennesssymmetry
ANRAATJ+BECJB  lemma:crossbar
RAATJ
BECJB
RAATH
RAAJH lemma:ray3
EEACAH  lemma:congruencesymmetric
COACH  assumption 
 COHAC  lemma:collinearorder
 NEAH   lemma:raystrict
 NEHA   lemma:inequalitysymmetric
 COAJH  lemma:rayimpliescollinear
 COHAJ  lemma:collinearorder
 COACJ  lemma:collinear4
 COCJB  defn:collinear
 COCJA  lemma:collinearorder
 NECJ   lemma:betweennotequal
 COJBA  lemma:collinear4
 COATJ  lemma:rayimpliescollinear
 COJAT  lemma:collinearorder
 COJAB  lemma:collinearorder
 NEAJ   lemma:raystrict
 NEJA   lemma:inequalitysymmetric
 COATB  lemma:collinear4
 COBAT  lemma:collinearorder
NCACH  reductio
TRACH  defn:triangle
ISACH   defn:isosceles
EAACHAHC proposition:05
ORBEAHJ|EQJH|BEAJH  lemma:ray1
cases LTHBCB:BEAHJ|EQJH|BEAJH
 case 1:BEAHJ
  COCJH   assumption
   COAHJ  defn:collinear
   COJHA  lemma:collinearorder
   COJHC  lemma:collinearorder
   NEHJ   lemma:betweennotequal
   NEJH   lemma:inequalitysymmetric
   COHAC  lemma:collinear4
   COACH  lemma:collinearorder
  NCCJH   reductio
  TRCJH   defn:triangle
  BEJHA   axiom:betweennesssymmetry
  AOJCHCHA  proposition:16
  COHCJ  assumption
   COCJH  lemma:collinearorder
  NCHCJ reductio
  EAHCJJCH  lemma:ABCequalsCBA
  AOHCJCHA  lemma:angleorderrespectscongruence2
  COAHC    assumption
   COACH   lemma:collinearorder
  NCAHC   reductio
  EAAHCCHA  lemma:ABCequalsCBA
  AOHCJAHC  lemma:angleorderrespectscongruence
  RAHBB    lemma:ray4
  BECJB
  EQCC     cn:equalityreflexive
  COCHJ    assumption
   COCJH   lemma:collinearorder
  NCCHJ   reductio
  EQCH assumption
   COCHJ  defn:collinear
  NECH reductio 
  NEHC lemma:inequalitysymmetric
  RAHCC  lemma:ray4
  EACHJCHJ  lemma:equalanglesreflexive
  NECJ   lemma:angledistinct
  NECH   lemma:angledistinct
  AOCHJCHB  defn:anglelessthan
  COCAH     assumption
   COACH    lemma:collinearorder
   NCACH
  NCCAH     reductio
  TRCAH     defn:triangle
  AOACHCHJ  proposition:16
  AOHCJAHC
  EAACHAHC
  AOHCJACH  lemma:angleorderrespectscongruence
  AOACHCHJ 
  AOHCJCHJ  lemma:angleordertransitive
  AOCHJCHB 
  AOHCJCHB  lemma:angleordertransitive
  EQHH     cn:equalityreflexive
  RACHH    lemma:ray4
  RACJB    lemma:ray4
  EAHCJHCJ  lemma:equalanglesreflexive
  EAHCJHCB  lemma:equalangleshelper
  EAHCBHCJ  lemma:equalanglessymmetric
  AOHCBCHB  lemma:angleorderrespectscongruence2
  COBHC      assumption
   COCJB     defn:collinear
   COBCH    lemma:collinearorder
   COBCJ    lemma:collinearorder
   NECB     lemma:betweennotequal
   NEBC     lemma:inequalitysymmetric
   COCHJ    lemma:collinear4 
  NCBHC     reductio
  TRBHC      defn:triangle
  EABHCCHB  lemma:ABCequalsCBA
  AOHCBBHC  lemma:angleorderrespectscongruence
  LTBHBC    proposition:19
  EEBHHB    cn:equalityreverse
  LTHBBC    lemma:lessthancongruence2
  EEBCCB    cn:equalityreverse
  LTHBCB    lemma:lessthancongruence
 qedcase
 case 2:EQJH
  BECHB  cn:equalitysub
  BEBHC  axiom:betweennesssymmetry
  EEBHHB  cn:equalityreverse
  LTHBBC defn:lessthan
  EEBCCB  cn:equalityreverse
  LTHBCB   lemma:lessthancongruence
 qedcase
 case 3:BEAJH
  BEHJA     axiom:betweennesssymmetry
  COCJH   assumption
   COAHJ  defn:collinear
   COJHA  lemma:collinearorder
   COJHC  lemma:collinearorder
   NEHJ   lemma:betweennotequal
   NEJH   lemma:inequalitysymmetric
   COHAC  lemma:collinear4
   COACH  lemma:collinearorder
  NCCJH   reductio
  COHCB     assumption
   COCJB     defn:collinear
   COBCJ    lemma:collinearorder
   COBCH    lemma:collinearorder
   NECB     lemma:betweennotequal
   NEBC     lemma:inequalitysymmetric
   COCHJ    lemma:collinear4  
   COCJH    lemma:collinearorder
   NCCJH      
  NCHCB     reductio
  EQHH     cn:equalityreflexive
  EQAA     cn:equalityreflexive
  EQCH     assumption
   COCHB   defn:collinear
   COHCB   lemma:collinearorder
  NECH   reductio
  RACAA     lemma:ray4
  EAHCBHCB  lemma:equalanglesreflexive
  RACBJ     lemma:ray4
  RACHH     lemma:ray4
  EAHCBHCJ  lemma:equalangleshelper
  BEHJA     axiom:betweennesssymmetry
  AOHCBHCA  defn:anglelessthan
  COBCH  assumption
   COHCB  lemma:collinearorder
  NCBCH  reductio
  EABCHHCB  lemma:ABCequalsCBA
  AOBCHHCA  lemma:angleorderrespectscongruence2
  NCACH
  EAACHHCA   lemma:ABCequalsCBA
  AOBCHACH  lemma:angleorderrespectscongruence
  EAACHAHC 
  EAAHCACH  lemma:equalanglessymmetric
  AOBCHAHC  lemma:angleorderrespectscongruence
  COAHC    assumption
   COACH   lemma:collinearorder
  NCAHC   reductio
  EAAHCCHA  lemma:ABCequalsCBA
  EQCC     cn:equalityreflexive
  EQBB     cn:equalityreflexive
  NEHB     lemma:angledistinct
  NEHC     lemma:angledistinct
  NEHA     lemma:angledistinct
  RAHCC    lemma:ray4
  RAHBB     lemma:ray4
  RAHAJ     lemma:ray4
  EAAHCCHJ   lemma:equalangleshelper
  BECJB
  AOAHCCHB  defn:anglelessthan
  COBHC assumption
   COHCB  lemma:collinearorder
  NCBHC   reductio
  EABHCCHB  lemma:ABCequalsCBA
  AOAHCBHC   lemma:angleorderrespectscongruence
  AOBCHBHC   lemma:angleordertransitive
  COHCB assumption
   COBHC  lemma:collinearorder
  NCHCB  reductio
  EAHCBBCH  lemma:ABCequalsCBA
  AOHCBBHC  lemma:angleorderrespectscongruence2
  TRBHC   defn:triangle
  LTBHBC  proposition:19
  EEBHHB  cn:equalityreverse
  LTHBBC   lemma:lessthancongruence2
  EEBCCB   cn:equalityreverse
  LTHBCB   lemma:lessthancongruence
 qedcase
LTHBCB cases 
EEHBFE
EEFEEF  cn:equalityreverse
EEHBEF  lemma:congruencetransitive
LTEFCB  lemma:lessthancongruence2
EECBBC  cn:equalityreverse
LTEFBC  lemma:lessthancongruence