reserve p,q,r for FinSequence,
  x,y for object;

theorem Th7:
  for R being Relation, a,b being object st
    [a,b] in R holds <*a,b*> is RedSequence of R
proof
  let R be Relation, a,b be object;
  assume
A1: [a,b] in R;
  set p = <*a,b*>;
  thus len p > 0;
  let i be Nat;
  assume that
A2: i in dom p and
A3: i+1 in dom p;
  len p = 1+1 by FINSEQ_1:44;
  then i+1 <= 1+1 by A3,Lm1;
  then
A4: i <= 1 by XREAL_1:6;
  i >= 1 by A2,Lm1;
  then p.1 = a & i = 1 by A4,XXREAL_0:1;
  hence thesis by A1;
end;
