# Metamathematic: Cover the case if X=Y

I want to formalize: "If X is less than Y, Then U is equal to Y ", and have been told that $$\bf [\forall V \sim X=(Y+V)]U=Y$$ does not cover the case X=Y. Therefore I have rewritten it as

$$\bf [\forall V \sim X=(Y+V)][\sim X=Y]U=Y.$$ Is this okay using basic meta math?

• Your syntax for logical formulas is quite unusual. From context it looks like you're writing $[P]Q$ for "if $P$ then $Q$", which is usually notated $P\Rightarrow Q$ or $P\to Q$ or (slightly old-fashioned) $P\supset Q$? – Henning Makholm Mar 30 '16 at 12:03
• Yes, that is correct. It is a bit diffrent but you have understod it correct. – ZaoZhen Mar 30 '16 at 12:10