Description: The index value of the Base slot is less than the index value of the .ef slot. (Contributed by AV, 21-Sep-2020) (Proof shortened by AV, 30-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | baseltedgf | |- ( Base ` ndx ) < ( .ef ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1nn | |- 1 e. NN |
|
| 2 | 8nn0 | |- 8 e. NN0 |
|
| 3 | 1nn0 | |- 1 e. NN0 |
|
| 4 | 1lt10 | |- 1 < ; 1 0 |
|
| 5 | 1 2 3 4 | declti | |- 1 < ; 1 8 |
| 6 | basendx | |- ( Base ` ndx ) = 1 |
|
| 7 | edgfndx | |- ( .ef ` ndx ) = ; 1 8 |
|
| 8 | 5 6 7 | 3brtr4i | |- ( Base ` ndx ) < ( .ef ` ndx ) |