Description: The slot for the base set is not the slot for the Euclidean function in an extensible structure. (Contributed by Thierry Arnoux, 9-Nov-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | basendxneufndx | |- ( Base ` ndx ) =/= ( EuclF ` ndx ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | basendxnn | |- ( Base ` ndx ) e. NN |
|
| 2 | 1 | nnrei | |- ( Base ` ndx ) e. RR |
| 3 | 2nn | |- 2 e. NN |
|
| 4 | 1nn0 | |- 1 e. NN0 |
|
| 5 | 1lt10 | |- 1 < ; 1 0 |
|
| 6 | 3 4 4 5 | declti | |- 1 < ; 2 1 |
| 7 | basendx | |- ( Base ` ndx ) = 1 |
|
| 8 | eufndx | |- ( EuclF ` ndx ) = ; 2 1 |
|
| 9 | 6 7 8 | 3brtr4i | |- ( Base ` ndx ) < ( EuclF ` ndx ) |
| 10 | 2 9 | ltneii | |- ( Base ` ndx ) =/= ( EuclF ` ndx ) |