theorem Th37:
  H is being_membership implies H = (Var1 H) 'in' Var2 H
proof
  assume
A1: H is being_membership;
  then consider x,y such that
A2: H = x 'in' y;
  <*1*>^<*x*>^<*y*> = <*1,x,y*> by FINSEQ_1:def 10;
  then
A3: H.2 = x & H.3 = y by A2;
A4: H is atomic by A1;
  then H.2 = Var1 H by Def28;
  hence thesis by A2,A4,A3,Def29;
end;
