reserve x,X for set,
        r,r1,r2,s for Real,
        i,j,k,m,n for Nat;
reserve p,q for Point of TOP-REAL n;

theorem Th26:
 1 <= i & i < j & j <= n implies
   Mx2Tran Rotation(i,j,n,r) is {i,j}-support-yielding
proof
  set M=Mx2Tran Rotation(i,j,n,r);
  assume A1: 1<=i & i<j & j<=n;
  let f be Function,x be set;
  assume that
  A2: f in dom M and
  A3: M.f.x<>f.x;
  reconsider p=f as Point of TOP-REAL n by A2,FUNCT_2:52;
  len p=n by CARD_1:def 7;
  then A4: dom p=Seg n by FINSEQ_1:def 3;
  len(M.p)=n by CARD_1:def 7;
  then A5: dom(M.p)=Seg n by FINSEQ_1:def 3;
  per cases;
  suppose A6: not x in Seg n;
    then M.p.x={} by A5,FUNCT_1:def 2;
    hence thesis by A3,A4,A6,FUNCT_1:def 2;
  end;
  suppose A7: x in Seg n;
    M.p.x<>p.x by A3;
    then x=i or x=j by A1,A7,Th20;
    hence thesis by TARSKI:def 2;
  end;
end;
