reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;
reserve i,j,k for Element of ARS_01;
reserve l,m,n for Element of ARS_02;
reserve A for set;

theorem LmA:
  x <> y & (for a,b holds a ==> b iff a = x)
  implies y is normform & x is normalizable
  proof
    assume
Z0: x <> y;
    assume
Z2: for a,b holds a ==> b iff a = x;
    thus y is normform by Z0,Z2;
    take y; thus y is normform by Z0,Z2;
    thus thesis by Z2,Th2;
  end;
