Description: The index of the slot for the base set is less then the index of the slot for the distance in an extensible structure. Formerly part of proof for tmslem . (Contributed by AV, 28-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxltdsndx | |- ( Base ` ndx ) < ( dist ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1nn | |- 1 e. NN |
|
| 2 | 2nn0 | |- 2 e. NN0 |
|
| 3 | 1nn0 | |- 1 e. NN0 |
|
| 4 | 1lt10 | |- 1 < ; 1 0 |
|
| 5 | 1 2 3 4 | declti | |- 1 < ; 1 2 |
| 6 | basendx | |- ( Base ` ndx ) = 1 |
|
| 7 | dsndx | |- ( dist ` ndx ) = ; 1 2 |
|
| 8 | 5 6 7 | 3brtr4i | |- ( Base ` ndx ) < ( dist ` ndx ) |