reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;
reserve f,g for differentiable Function of REAL,REAL;
reserve L for non empty ZeroStr;
reserve x for Element of L;

theorem Th25:
  m <> n implies seq(n,x).m = 0.L
  proof
    assume m <> n;
    hence seq(n,x).m = (0_.L).m by FUNCT_7:32
    .= 0.L by ORDINAL1:def 12,FUNCOP_1:7;
  end;
