Description: The index of the slot for the distance is not the index of other slots. Formerly part of proof for cnfldfun . (Contributed by AV, 11-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | slotsdifplendx | |- ( ( *r ` ndx ) =/= ( le ` ndx ) /\ ( TopSet ` ndx ) =/= ( le ` ndx ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 4re | |- 4 e. RR |
|
| 2 | 4lt10 | |- 4 < ; 1 0 |
|
| 3 | 1 2 | ltneii | |- 4 =/= ; 1 0 |
| 4 | starvndx | |- ( *r ` ndx ) = 4 |
|
| 5 | plendx | |- ( le ` ndx ) = ; 1 0 |
|
| 6 | 4 5 | neeq12i | |- ( ( *r ` ndx ) =/= ( le ` ndx ) <-> 4 =/= ; 1 0 ) |
| 7 | 3 6 | mpbir | |- ( *r ` ndx ) =/= ( le ` ndx ) |
| 8 | 9re | |- 9 e. RR |
|
| 9 | 9lt10 | |- 9 < ; 1 0 |
|
| 10 | 8 9 | ltneii | |- 9 =/= ; 1 0 |
| 11 | tsetndx | |- ( TopSet ` ndx ) = 9 |
|
| 12 | 11 5 | neeq12i | |- ( ( TopSet ` ndx ) =/= ( le ` ndx ) <-> 9 =/= ; 1 0 ) |
| 13 | 10 12 | mpbir | |- ( TopSet ` ndx ) =/= ( le ` ndx ) |
| 14 | 7 13 | pm3.2i | |- ( ( *r ` ndx ) =/= ( le ` ndx ) /\ ( TopSet ` ndx ) =/= ( le ` ndx ) ) |