Description: Define "less than or equal to" ordering extractor for posets and related structures. We use ; 1 0 for the index to avoid conflict with 1 through 9 used for other purposes. (Contributed by NM, 4-Sep-2011) (Revised by Mario Carneiro, 14-Aug-2015) (Revised by AV, 9-Sep-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-ple | ⊢ le = Slot ; 1 0 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cple | ⊢ le | |
| 1 | c1 | ⊢ 1 | |
| 2 | cc0 | ⊢ 0 | |
| 3 | 1 2 | cdc | ⊢ ; 1 0 |
| 4 | 3 | cslot | ⊢ Slot ; 1 0 |
| 5 | 0 4 | wceq | ⊢ le = Slot ; 1 0 |