Definition df-gte

Description: Define the 'greater than or equal' predicate over the reals. Defined in ISO 80000-2:2009(E) operation 2-7.10. It is used as a primitive in the "NIST Digital Library of Mathematical Functions" , front introduction, "Common Notations and Definitions" section at http://dlmf.nist.gov/front/introduction#Sx4 . This relation is merely the converse of the 'less than or equal to' relation defined by df-le .

We do not write this as ( x >_ y <-> y <_ x ) , and similarly we do not write `>as ( x > y <-> y < x ) , because these are not definitional axioms as understood by mmj2 (those definitions will be flagged as being "potentially non-conservative"). We could write them this way: |- > = { <. x , y >. | ( ( x e. RR* /\ y e. RR* ) /\ y < x ) } and |- >_ = { <. x , y >. | ( ( x e. RR* /\ y e. RR* ) /\ y <_ x ) } but these are very complicated. This definition of >_ , and the similar one for > ( df-gt ), are a bit strange when you see them for the first time, but these definitions are much simpler for us to process and are clearly conservative definitions. (My thanks to Mario Carneiro for pointing out this simpler approach.) See gte-lte for a more conventional expression of the relationship between < and > ` . As a stylistic issue, set.mm prefers 'less than' instead of 'greater than' to reduce the number of conversion steps. Thus, we discourage its use, but include its definition so that thereis a formal definition of this symbol.

(Contributed by David A. Wheeler, 10-May-2015) (New usage is discouraged.)

	Ref	Expression
Assertion	df-gte	|- >_ = `' <_

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cge-real	|- >_
1		cle	|- <_
2	1	ccnv	|- `' <_
3	0 2	wceq	|- >_ = `' <_