Step |
Hyp |
Ref |
Expression |
1 |
|
s4cli |
|- <" A B C D "> e. Word _V |
2 |
|
lsw |
|- ( <" A B C D "> e. Word _V -> ( lastS ` <" A B C D "> ) = ( <" A B C D "> ` ( ( # ` <" A B C D "> ) - 1 ) ) ) |
3 |
1 2
|
mp1i |
|- ( D e. V -> ( lastS ` <" A B C D "> ) = ( <" A B C D "> ` ( ( # ` <" A B C D "> ) - 1 ) ) ) |
4 |
|
s4len |
|- ( # ` <" A B C D "> ) = 4 |
5 |
4
|
oveq1i |
|- ( ( # ` <" A B C D "> ) - 1 ) = ( 4 - 1 ) |
6 |
|
4m1e3 |
|- ( 4 - 1 ) = 3 |
7 |
5 6
|
eqtri |
|- ( ( # ` <" A B C D "> ) - 1 ) = 3 |
8 |
7
|
fveq2i |
|- ( <" A B C D "> ` ( ( # ` <" A B C D "> ) - 1 ) ) = ( <" A B C D "> ` 3 ) |
9 |
8
|
a1i |
|- ( D e. V -> ( <" A B C D "> ` ( ( # ` <" A B C D "> ) - 1 ) ) = ( <" A B C D "> ` 3 ) ) |
10 |
|
s4fv3 |
|- ( D e. V -> ( <" A B C D "> ` 3 ) = D ) |
11 |
3 9 10
|
3eqtrd |
|- ( D e. V -> ( lastS ` <" A B C D "> ) = D ) |