reserve r,t for Real;
reserve i for Integer;
reserve k,n for Nat;
reserve p for Polynomial of F_Real;
reserve e for Element of F_Real;
reserve L for non empty ZeroStr;
reserve z,z0,z1,z2 for Element of L;

theorem Th24:
  3 <= n implies <%z0,z1,z2%>.n = 0.L
  proof
    assume
A1: 3 <= n;
    then
A2: n <> 0 & n <> 1 & n <> 2;
    hence <%z0,z1,z2%>.n = (0_.L +* (0,z0) +* (1,z1)).n by FUNCT_7:32
    .= (0_.L +* (0,z0)).n by A2,FUNCT_7:32
    .= (0_.L).n by A1,FUNCT_7:32
    .= 0.L by ORDINAL1:def 12,FUNCOP_1:7;
  end;
