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Mirrors > Home > MPE Home > Th. List > df-sra | Structured version Visualization version Unicode version |
Description: Given any subring of a ring, we can construct a left-algebra by regarding the elements of the subring as scalars and the ring itself as a set of vectors. (Contributed by Mario Carneiro, 27-Nov-2014.) (Revised by Thierry Arnoux, 16-Jun-2019.) |
Ref | Expression |
---|---|
df-sra |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csra 18440 |
. 2
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2 | vw |
. . 3
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3 | cvv 3057 |
. . 3
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4 | vs |
. . . 4
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5 | 2 | cv 1454 |
. . . . . 6
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6 | cbs 15170 |
. . . . . 6
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7 | 5, 6 | cfv 5601 |
. . . . 5
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8 | 7 | cpw 3963 |
. . . 4
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9 | cnx 15167 |
. . . . . . . . 9
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10 | csca 15242 |
. . . . . . . . 9
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11 | 9, 10 | cfv 5601 |
. . . . . . . 8
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12 | 4 | cv 1454 |
. . . . . . . . 9
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13 | cress 15171 |
. . . . . . . . 9
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14 | 5, 12, 13 | co 6315 |
. . . . . . . 8
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15 | 11, 14 | cop 3986 |
. . . . . . 7
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16 | csts 15168 |
. . . . . . 7
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17 | 5, 15, 16 | co 6315 |
. . . . . 6
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18 | cvsca 15243 |
. . . . . . . 8
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19 | 9, 18 | cfv 5601 |
. . . . . . 7
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20 | cmulr 15240 |
. . . . . . . 8
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21 | 5, 20 | cfv 5601 |
. . . . . . 7
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22 | 19, 21 | cop 3986 |
. . . . . 6
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23 | 17, 22, 16 | co 6315 |
. . . . 5
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24 | cip 15244 |
. . . . . . 7
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25 | 9, 24 | cfv 5601 |
. . . . . 6
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26 | 25, 21 | cop 3986 |
. . . . 5
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27 | 23, 26, 16 | co 6315 |
. . . 4
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28 | 4, 8, 27 | cmpt 4475 |
. . 3
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29 | 2, 3, 28 | cmpt 4475 |
. 2
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30 | 1, 29 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: sraval 18448 |
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