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;

theorem Th18:
  m <> i & m <> k implies ((f,i):=(k,r)).m = f.m
proof
  assume that
A1: m <> i and
A2: m <> k;
  set fik = (f,i):=k;
  thus ((f,i):=(k,r)).m =fik.m by A2,FUNCT_7:32
    .=f.m by A1,FUNCT_7:32;
end;
