reserve

  k,n for Nat,
  x,y,X,Y,Z for set;

theorem
  for S1,S2 being IncProjStr for F1,F2 being IncProjMap over S1,S2 st
  the IncProjMap of F1 = the IncProjMap of F2 holds F1 is incidence_preserving
  implies F2 is incidence_preserving
proof
  let S1,S2 be IncProjStr;
  let F1,F2 be IncProjMap over S1,S2;
  assume that
A1: the IncProjMap of F1 = the IncProjMap of F2 and
A2: F1 is incidence_preserving;
  let A1 be POINT of S1;
  let L1 be LINE of S1;
  F2.A1 = F1.A1 & F2.L1 = F1.L1 by A1;
  hence thesis by A2;
end;
