reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem Th8:
  G is IncProjSp implies ex b,c st {b,c} on A & a,b,c are_mutually_distinct
proof
  assume
A1: G is IncProjSp;
  then consider b such that
A2: b on A & b<>a and
  b<>a by PROJRED1:8;
  consider c such that
A3: c on A & c <>a & c <>b by A1,PROJRED1:8;
  take b,c;
  thus thesis by A2,A3,INCSP_1:1,ZFMISC_1:def 5;
end;
