| Step |
Hyp |
Ref |
Expression |
| 1 |
|
1wlkd.p |
|- P = <" X Y "> |
| 2 |
|
1wlkd.f |
|- F = <" J "> |
| 3 |
2
|
fveq2i |
|- ( # ` F ) = ( # ` <" J "> ) |
| 4 |
|
s1len |
|- ( # ` <" J "> ) = 1 |
| 5 |
3 4
|
eqtri |
|- ( # ` F ) = 1 |
| 6 |
5
|
oveq2i |
|- ( 1 ..^ ( # ` F ) ) = ( 1 ..^ 1 ) |
| 7 |
|
fzo0 |
|- ( 1 ..^ 1 ) = (/) |
| 8 |
6 7
|
eqtri |
|- ( 1 ..^ ( # ` F ) ) = (/) |
| 9 |
8
|
imaeq2i |
|- ( P " ( 1 ..^ ( # ` F ) ) ) = ( P " (/) ) |
| 10 |
9
|
ineq2i |
|- ( ( P " { 0 , ( # ` F ) } ) i^i ( P " ( 1 ..^ ( # ` F ) ) ) ) = ( ( P " { 0 , ( # ` F ) } ) i^i ( P " (/) ) ) |
| 11 |
|
ima0 |
|- ( P " (/) ) = (/) |
| 12 |
11
|
ineq2i |
|- ( ( P " { 0 , ( # ` F ) } ) i^i ( P " (/) ) ) = ( ( P " { 0 , ( # ` F ) } ) i^i (/) ) |
| 13 |
|
in0 |
|- ( ( P " { 0 , ( # ` F ) } ) i^i (/) ) = (/) |
| 14 |
12 13
|
eqtri |
|- ( ( P " { 0 , ( # ` F ) } ) i^i ( P " (/) ) ) = (/) |
| 15 |
10 14
|
eqtri |
|- ( ( P " { 0 , ( # ` F ) } ) i^i ( P " ( 1 ..^ ( # ` F ) ) ) ) = (/) |