Description: The multiplication monoid has the same (if any) scalars as the original ring. Mostly to simplify pwsmgp . (Contributed by Mario Carneiro, 12-Mar-2015) (Revised by Mario Carneiro, 5-May-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mgpbas.1 | ||
mgpsca.s | |||
Assertion | mgpsca |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mgpbas.1 | ||
2 | mgpsca.s | ||
3 | eqid | ||
4 | 1 3 | mgpval | |
5 | scaid | ||
6 | scandxnplusgndx | ||
7 | 4 5 6 | setsplusg | |
8 | 2 7 | eqtri |