Description: A scalar polynomial is a polynomial. (Contributed by Stefan O'Rear, 28-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ply1scl.p | |- P = ( Poly1 ` R ) |
|
ply1scl.a | |- A = ( algSc ` P ) |
||
coe1scl.k | |- K = ( Base ` R ) |
||
ply1sclf.b | |- B = ( Base ` P ) |
||
Assertion | ply1sclf | |- ( R e. Ring -> A : K --> B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ply1scl.p | |- P = ( Poly1 ` R ) |
|
2 | ply1scl.a | |- A = ( algSc ` P ) |
|
3 | coe1scl.k | |- K = ( Base ` R ) |
|
4 | ply1sclf.b | |- B = ( Base ` P ) |
|
5 | 1 | ply1sca2 | |- ( _I ` R ) = ( Scalar ` P ) |
6 | 1 | ply1ring | |- ( R e. Ring -> P e. Ring ) |
7 | 1 | ply1lmod | |- ( R e. Ring -> P e. LMod ) |
8 | df-base | |- Base = Slot 1 |
|
9 | 8 3 | strfvi | |- K = ( Base ` ( _I ` R ) ) |
10 | 2 5 6 7 9 4 | asclf | |- ( R e. Ring -> A : K --> B ) |