reserve x,y,X for set,
  i,j,k,m,n for Nat,
  p for FinSequence of X,
  ii for Integer;
reserve G for Graph,
  pe,qe for FinSequence of the carrier' of G,
  p,q for oriented Chain of G,
  W for Function,
  U,V,e,ee for set,
  v1,v2,v3,v4 for Vertex of G;
reserve G for finite Graph,
  P,Q for oriented Chain of G,
  v1,v2,v3 for Vertex of G;
reserve G for finite oriented Graph,
  P,Q for oriented Chain of G,
  W for Function of (the carrier' of G), Real>=0,
  v1,v2,v3,v4 for Vertex of G;
reserve f,g,h for Element of REAL*,
  r for Real;
reserve G for oriented Graph,
  v1,v2 for Vertex of G,
  W for Function of (the carrier' of G), Real>=0;

theorem Th37:
  dom ((repeat(Relax(n)*findmin(n))).i.f) = dom ((repeat(Relax(n)*
  findmin(n))).(i+1).f)
proof
  set R=Relax(n), M=findmin(n), ff=(repeat (R*M)).i.f;
  thus dom ((repeat (R*M)).(i+1).f) = dom (R.(M.ff)) by Th22
    .= dom (M.ff) by Th35
    .= dom ff by Th33;
end;
