
theorem Th20:
  for A,B being reflexive non empty AltGraph,
  F being BimapStr over A,B st F is coreflexive for o being Object of B
  ex o9 being Object of A st F.o9 = o
proof
  let A,B be reflexive non empty AltGraph, F be BimapStr over A,B;
  assume F is coreflexive;
  then
A1: id the carrier of B c= (the ObjectMap of F).:id the carrier of A;
  let o be Object of B;
  reconsider oo = [o,o] as
  Element of [:the carrier of B,the carrier of B:] by ZFMISC_1:87;
  [o,o] in id the carrier of B by RELAT_1:def 10;
  then consider pp being Element of [:the carrier of A,the carrier of A:]
  such that
A2: pp in id the carrier of A and
A3: (the ObjectMap of F).pp = oo by A1,FUNCT_2:65;
  consider p,p9 being object such that
A4: pp = [p,p9] by RELAT_1:def 1;
A5: p = p9 by A2,A4,RELAT_1:def 10;
  reconsider p as Object of A by A2,A4,RELAT_1:def 10;
  take p;
  thus thesis by A3,A4,A5;
end;
