min(a_ and b_) := min(a,b);
min(a_ * b_) := If(a>0, a*min(b), If(a<0, a*max(b) ));
min(a_ + b_) := min(a)+min(b);
min(a_ - b_) := min(min(a)-min(b),min(a)+min(b));

min(sin(x_)):= -1;
min(cos(x_)):= -1;
min(tan(x_)):= -oo;
min(cot(x_)):= -oo;
min(sec(x_)):= -oo;
min(csc(x_)):= -oo;

min(asin(x_)):= -oo;
min(acos(x_)):= -oo;
min(atan(x_)):= -pi/2;
min(acot(x_)):= -pi/2;
min(asec(x_)):= -pi/2;
min(acsc(x_)):= -pi/2;

min(sinh(x_)):= -oo;
min(cosh(x_)):= 1;
min(tanh(x_)):= -1;
min(coth(x_)):= -1;
min(sech(x_)):= 0;
min(csch(x_)):= oo;

min(asinh(x_)):= -oo;
min(acosh(x_)):= -oo;
min(atanh(x_)):= -oo;
min(acoth(x_)):= -oo;
min(asech(x_)):= -oo;
min(acsch(x_)):= -oo;

min(exp(x_)):= 0;
min(log(x_)):= -oo;

min(e^x_):=0;
min(e^(x_^2)):=1;
min(x_^2):= 0;