Description: The 'greater than' relation is merely the converse of the 'less than or equal to' relation defined by df-lt . Defined in ISO 80000-2:2009(E) operation 2-7.12. See df-gte for a discussion on why this approach is used for the definition. See gt-lt and gt-lth for more conventional expression of the relationship between < and > .
As a stylistic issue, set.mm prefers 'less than or equal' instead of 'greater than or equal' 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, 19-Apr-2015) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-gt | ⊢ > = ◡ < |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cgt | ⊢ > | |
| 1 | clt | ⊢ < | |
| 2 | 1 | ccnv | ⊢ ◡ < |
| 3 | 0 2 | wceq | ⊢ > = ◡ < |