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Question: How to use substition with functions?

Question:How to use substition with functions?

KonstantinW 220 Maple 2016
May 15 2017
2

Consider substutition with use of a function:

subs(F(x,y)=f(x)+g(y), F(x,y));

As expected, Maple returns the proper answer:

f(x)+g(y)

But 

subs(F(x,y)=f(x)+g(y), F(x,x));

returns 

F(x,x)

How to force Maple recognize F as a function, in order to obtain

f(x)+g(x)

in return?

The functions algsubs, applyrule work in the same way.
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