reserve x,y,t for Real;

theorem
  x>=1 implies cosh1"(x)=sinh"(sqrt(x^2-1))
proof
  assume
A1: x>=1;
  then x^2-1>=0 by Lm3;
  then sinh"(sqrt(x^2-1)) =log(number_e,((sqrt(x^2-1))+sqrt((x^2-1)+1))) by
SQUARE_1:def 2
    .=log(number_e,((sqrt(x^2-1))+x)) by A1,SQUARE_1:22;
  hence thesis;
end;
