Description: The multiplication operation of the ordered power series structure. (Contributed by Mario Carneiro, 8-Feb-2015) (Revised by Mario Carneiro, 30-Aug-2015)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | opsrbas.s | |- S = ( I mPwSer R ) |
|
| opsrbas.o | |- O = ( ( I ordPwSer R ) ` T ) |
||
| opsrbas.t | |- ( ph -> T C_ ( I X. I ) ) |
||
| Assertion | opsrmulr | |- ( ph -> ( .r ` S ) = ( .r ` O ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opsrbas.s | |- S = ( I mPwSer R ) |
|
| 2 | opsrbas.o | |- O = ( ( I ordPwSer R ) ` T ) |
|
| 3 | opsrbas.t | |- ( ph -> T C_ ( I X. I ) ) |
|
| 4 | df-mulr | |- .r = Slot 3 |
|
| 5 | 3nn | |- 3 e. NN |
|
| 6 | 3lt10 | |- 3 < ; 1 0 |
|
| 7 | 1 2 3 4 5 6 | opsrbaslem | |- ( ph -> ( .r ` S ) = ( .r ` O ) ) |