reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;

theorem Th80:
  for x,L1,L2 st L1 _|_ L2 holds ex L0 st x in L0 & L0 _|_ L2 & L0 // L1
proof
  let x,L1,L2;
  assume
A1: L1 _|_ L2;
  then L1 is being_line by Th67;
  then consider L0 such that
A2: x in L0 & L0 // L1 by Th72;
  take L0;
  thus thesis by A1,A2,Th61;
end;
