reserve f for PartFunc of REAL-NS 1,REAL-NS 1;
reserve g for PartFunc of REAL,REAL;
reserve x for Point of REAL-NS 1;
reserve y for Real;
reserve m,n for non zero Nat;
reserve i,j for Nat;
reserve f for PartFunc of REAL-NS n,REAL-NS 1;
reserve g for PartFunc of REAL n,REAL;
reserve x for Point of REAL-NS n;
reserve y for Element of REAL n;

theorem Th13:
  f=<>*g & x=y implies <>*(g*reproj(i,y)) = f*reproj(i,x)
proof
  reconsider h=proj(1,1)qua Function" as Function of REAL,REAL 1 by Th2;
  assume that
A1: f=<>*g and
A2: x=y;
  reproj(i,y)*proj(1,1) = reproj(i,x) by A2,Th12;
  then (h*g)*reproj(i,y)*proj(1,1) = f*reproj(i,x) by A1,RELAT_1:36;
  hence thesis by RELAT_1:36;
end;
