reserve f,f1,f2,g for PartFunc of REAL,REAL;
reserve A for non empty closed_interval Subset of REAL;
reserve p,r,x,x0 for Real;
reserve n for Element of NAT;
reserve Z for open Subset of REAL;

theorem Th31:
  cosh`|REAL = sinh
proof
  for x st x in REAL holds diff(cosh,x)=sinh.x by SIN_COS2:35;
  hence thesis by FDIFF_1:def 7,SIN_COS2:30,35;
end;
