reserve S for IncStruct;
reserve A,B,C,D for POINT of S;
reserve L for LINE of S;
reserve P for PLANE of S;
reserve F,G for Subset of the Points of S;

theorem
  G c= F & F is linear implies G is linear
proof
  assume that
A1: G c= F and
A2: F is linear;
  consider L such that
A3: F on L by A2;
  take L;
  let A be POINT of S;
  assume A in G;
  hence thesis by A1,A3;
end;
