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
  A= [.0,1.] implies integral(cosh,A) = (number_e^2 - 1)/(2*number_e)
proof
  assume A=[.0,1.];
  then A=[.0,jj.];
  then upper_bound A=1 & lower_bound A=0 by Th37;
  then integral(cosh,A) = sinh.1 -0 by Th57,SIN_COS2:16
    .= (number_e^2 - 1)/(2*number_e) by Th17;
  hence thesis;
end;
