# Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me.

Simplify[a == b, {a == {1}, b == {1}}]

a == b


does not evaluate the equality, while

Simplify[a == b, {a == 1, b == 1}]

True


does. What is the explanation?

Another one:

Simplify[a/b == e/f, {a/b == c/d, c/d == e/f}]

a/b == e/f

• Even FullSimplify can't do this. But I found this: In[] Simplify[a == b, {a == c[{1}], b == c[{1}]}] Out[] True – wacharin wichiramala Mar 15 '16 at 8:53
• Perhaps an even more succinct example is comparing Simplify[a, a == {1}] to Simplify[a, a == 1] – Jason B. Mar 15 '16 at 9:16
• List equality/simplification vs number equality/simplification, interesting. – barrycarter Mar 15 '16 at 15:13
• But isn't this a matter of {1} not being "more simple" than a? Simplify does what it says: it simplifies an expression according to some "aesthetic". One thing that it does is to minimize the LeafCount of the expression, and LeafCount@a is 1 whereas LeafCount@{1} is 2. @JasonB. – march Mar 15 '16 at 16:52
• @JasonB and OP: I recommend putting those examples into the original post, because especially the OP's version with c[{1}] is confusing (although I think my previous comment accounts for JasonB's example and it might account for the OP's). – march Mar 15 '16 at 16:58