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
  integral(r(#)cosh,A) = r*sinh.(upper_bound A) - r*sinh.(lower_bound A)
proof
A1: [#]REAL is open Subset of REAL;
  cosh|A is continuous & cosh|A is bounded by Lm10,Lm16,INTEGRA5:10;
  hence thesis by A1,Lm10,Th30,Th68,INTEGRA5:11,SIN_COS2:34;
end;
