Description: Obsolete version of zlmbas as of 3-Nov-2024. Group operation of a ZZ -module. (Contributed by Mario Carneiro, 2-Oct-2015) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | zlmbas.w | |- W = ( ZMod ` G ) |
|
| zlmplusg.2 | |- .+ = ( +g ` G ) |
||
| Assertion | zlmplusgOLD | |- .+ = ( +g ` W ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zlmbas.w | |- W = ( ZMod ` G ) |
|
| 2 | zlmplusg.2 | |- .+ = ( +g ` G ) |
|
| 3 | df-plusg | |- +g = Slot 2 |
|
| 4 | 2nn | |- 2 e. NN |
|
| 5 | 2lt5 | |- 2 < 5 |
|
| 6 | 1 3 4 5 | zlmlemOLD | |- ( +g ` G ) = ( +g ` W ) |
| 7 | 2 6 | eqtri | |- .+ = ( +g ` W ) |