Description: A vector of a module with indices from 0 to N - 1 is a word over the scalars of the module. (Contributed by SN, 31-Aug-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | frlmfzowrd.w | |- W = ( K freeLMod ( 0 ..^ N ) ) |
|
frlmfzowrd.b | |- B = ( Base ` W ) |
||
frlmfzowrd.s | |- S = ( Base ` K ) |
||
Assertion | frlmfzowrd | |- ( X e. B -> X e. Word S ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frlmfzowrd.w | |- W = ( K freeLMod ( 0 ..^ N ) ) |
|
2 | frlmfzowrd.b | |- B = ( Base ` W ) |
|
3 | frlmfzowrd.s | |- S = ( Base ` K ) |
|
4 | ovex | |- ( 0 ..^ N ) e. _V |
|
5 | 1 3 2 | frlmbasf | |- ( ( ( 0 ..^ N ) e. _V /\ X e. B ) -> X : ( 0 ..^ N ) --> S ) |
6 | 4 5 | mpan | |- ( X e. B -> X : ( 0 ..^ N ) --> S ) |
7 | iswrdi | |- ( X : ( 0 ..^ N ) --> S -> X e. Word S ) |
|
8 | 6 7 | syl | |- ( X e. B -> X e. Word S ) |