 reserve X,a,b,c,x,y,z,t for set;
 reserve R for Relation;

theorem Th13:
  for L1,L2 be RelStr st the RelStr of L1 = the RelStr of L2 &
    L1 is mediate holds L2 is mediate
  proof
    let L1, L2 be RelStr;
    assume
A1: the RelStr of L1 = the RelStr of L2;
    assume L1 is mediate; then
    the InternalRel of L1 is_mediate_in the carrier of L1 by ROUGHS_2:def 7;
    hence thesis by A1,ROUGHS_2:def 7;
  end;
