How to check the positivity function?

I can't prove the positivity of the function:

y = x1 - x2 + sin(x1)
such that:
0<x1<0.0001
0<x2<0.0001
x1>x2 

My matlab code is:

x = sym('x', [1 2], 'real') 
assume(0.0001>x>0 & x(1)>x(2))
y = x(1) - x(2) + sin(x(1))
isAlways(y>=0)

%Below the responde from command window

Warning: Unable to prove '0 <= x1 - x2 + sin(x1)'.

> In symengine

In sym/isAlways (line 42)

Why Matlab can't prove the positivity of the function y?

I can prove that "x(1)-x(2)" and "sin(x(1))" are positive, I don't know why I can't prove the positivity of the sum of positivity term.

Any kind of help is appreciate, I'm stucked on this for hours..

Answer 1

[Walter Roberson]

Eh. So split it up. x1 strictly > x2 impliex x1 - x2 > 0

x1 > 0 and x1 < pi implies sin(x1) > 0

the sum of two positive quantities is positive.

x = sym('x', [1 2], 'real') 

x = 

assume(0.0001>x>0 & x(1)>x(2))
y1 = x(1) + x(2)

y1 = 

y2 = sin(x(1))

y2 = 

isAlways(y1 > 0)

ans = logical
   1

isAlways(y2 > 0)

ans = logical
   1

syms y3 y4   %y3 is the positive quantity y1, y4 is the positive quantity sin(x(1))
assume(y3>0 & y4>0)
isAlways(y3+y4 > 0)

ans = logical
   1