Sindbad~EG File Manager

NEAB
ICAJ
ICBJ
CIJCPQ
BEEMF
EEEMPQ
EEEMMF
OREQAC|LTCAPQ  lemma:insideor
OREQBC|LTCBPQ  lemma:insideor
EEPQEM   lemma:congruencesymmetric
EEEMEM   cn:congruencereflexive
LTEMEF   defn:lessthan

cases LTABEF:EQAC|LTCAPQ
 case 1:EQAC
  cases LTABEF:EQBC|LTCBPQ
   case 1:EQBC
    NOLTABEF  assumption
     EQAB  cn:equalitytransitive
     NEAB
    LTABEF reductio
   qedcase
   case 2:LTCBPQ
    LTABPQ   cn:equalitysub
    LTABEM   lemma:lessthancongruence
    LTABEF   lemma:lessthantransitive
   qedcase
  LTABEF cases
 qedcase
 case 2:LTCAPQ
  cases LTABEF:EQBC|LTCBPQ
   case 1:EQBC
	LTCAPQ  
	EEBAAB cn:equalityreverse
    LTBAPQ  cn:equalitysub
    LTABPQ  lemma:lessthancongruence2
    LTABEM  lemma:lessthancongruence
    LTABEF  lemma:lessthantransitive
   qedcase     
   case 2:LTCBPQ
    EECAAC   cn:equalityreverse
    LTACPQ   lemma:lessthancongruence2
    LTACEM   lemma:lessthancongruence
    EEACCA   cn:equalityreverse
    LTCAEM   lemma:lessthancongruence2
    EEEMME   cn:equalityreverse
	LTCAME   lemma:lessthancongruence
	LTCBPQ
	EEPQMF   lemma:congruencetransitive
	LTCBMF   lemma:lessthancongruence
	NEMG
	RAMEG+EEMGCA   lemma:layoff
	RAMEG
	EEMGCA
	LTACEM
	LRCAEM    lemma:lessthancongruence2
	EECAMG    lemma:congruencesymmetric
	LTMGME    lemma:lessthancongruence2
	ORBEMGE|EQGE|BEMEG   lemma:ray2
	NOBEMGE   assumption
	 cases BEMGE:BEMGE|EQGE|BEMEG
	  case 1:BEMGE
	  qedcase
	  case 2:EQGE
	   NOBEMGE  assumption
	    LTMEME  cn:equalitysub
	    NOLTMEME  lemma:trichotomy2
	   BEMGE  reductio
	  qedcase
	  case 3:BEMEG
	    
	   
	BEMGE     reductio
	EEMGCA
	ANBEMHF+EEMHCB  lemma:layoff
	BEMHF
	EEMHCB
	BEEGM   axiom:betweennesssymmetry
	BEEMF   lemma:3.5b
	BEGMF   lemma:3.5b
	BEGMH   axiom:innertransitivity
	EEACGM  lemma:doublereverse
	EECBMH   lemma:congruencesymmetric
	LTABGH   lemma:triangleinequality
	EEGCHGH  cn:congruencereflexive
	LTGHGF   defn:lessthan
	EEGFFG   cn:equalityreverse
	EEFGFG   cn:congruencereflexive
	LTFGFE   defn:lessthan
	LTGFFE   lemma:lessthancongruence2
	LTGHFE   lemma:lessthangransitive
	EEFEEF   cn:congruencereflexive
	LTGHEF   lemma:lessthancongruence
	LTABEF   lemma:lessthantransitive
   qedcase
  LTABEF cases 
 qedcase
LTABEF cases