# How can I check if one expression implies another?

Say I have one expression, for example $x^3-3 + c = y$, and I want to check if it implies another with some set of explicitly stated assumptions. With the previous example, assuming all variables are positive real numbers, we might ask if $x^3-3 + c = y$ implies $c = -x^3 + y$. This example is trivial, but I'd like to do the same where, perhaps, choices can be made about the use of various special functions or identities and there can also be inequalities.

Is there something like ImpliesQ[{exp1,exp2}]?

• Implies[x^3 - 3 + c == y, c == y - x^3] // Reduce
– ciao
Feb 16, 2014 at 3:45
• @rasher Wham. :) Feb 16, 2014 at 5:55
• @Nasser The example I choose was a poor one... I was thinking more along the lines of there being some choice for special functions / etc. in one derivation vs. another, and then making sure that the results are the same. Feb 16, 2014 at 5:56

Simplify[c == y - x^3, Assumptions -> x^3 - 3 + c == y]

Simplify[c == y - x^3 + 3, Assumptions -> x^3 - 3 + c == y]

It's simply AssumptionsImpliesQ`.