Substitute function definitions in SymPy expressions

[vladislavstrmlt]

Let's say I have an expression, such as sympy.core.relational.Equality containing an "unknown" function, like so.

import sympy as sp

f = sp.Function(sp.Symbol("f", real=True))
x, y = sp.symbols(("x","y"), real=True)

equation = sp.Eq(f(x+y), f(x)+y)  # The functional equation f(x+y) = f(x)+y

My question is: Is there any way to substitute this function with its definition, for example if I suddenly know that it's $f(x)=x+2.$ The below doesn't work, as it only replaces exactly f(x), with x+2 not f(x+y) with x+y+2

equation.subs(f(x), x+2)

This returns Eq(f(x+y), x+2 + y), rather than the expected Eq(x+y+2, x+2 + y) (which then evaluates to sympy.logic.boolalg.BooleanTrue).

Essentially, I am trying to make a "check" method to check if a given function actually satisfies the condition, where it for example would return True when given the above, since it satisfies it. (I know this is probably not possible completely in general covering all edge cases by Richardson's theorem, but it's gotta be possible to do the above(?))

Any help, links or anything is appreciated 🌟

[oscarbenjamin]

You can do this with replace:

In [7]: a = Wild('a')

In [8]: f(x+y).replace(f(a), a+2)
Out[8]: x + y + 2

In [9]: equation.replace(f(a), a + 2)
Out[9]: True