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CIKFPQ
EEFDPQ
EEFMPQ
BEDFM
BEDNM
NEDF  lemma:betweennotequal
NEFD  lemma:inequalitysymmetric
NOORBEDNF|BEFNM|EQFN assumption
 ANNOBEDNF+NOBEFNM+NEFN
 NOBEDNF
 NOBEFNM
 NEFN
 BEDFN  assumption
  BEFNM  lemma:3.6a
 NOBEDFN reductio
 EQFN  axiom:connectivity
ORBEDNF|BEFNM|EQFN reductio
EEFNFN cn:congruencereflexive
cases ICNK:BEDNF|BEFNM|EQFN
 case 1:BEDNF
  BEFND axiom:betweennesssymmetry
  ANBEFND+EEFDPQ+EEFNFN
  ICNK  defn:inside
 qedcase
 case 2:BEFNM
  ANBEFNM+EEFMPQ+EEFNFN
  ICNK  defn:inside
 qedcase
 case 3:EQFN
  EQNF  lemma:equalitysymmetric
  ICNK  defn:inside
 qedcase
ICNK cases

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