Description: Group operation of a ZZ -module. (Contributed by Mario Carneiro, 2-Oct-2015) (Revised by AV, 3-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | zlmbas.w | |- W = ( ZMod ` G ) |
|
| zlmplusg.2 | |- .+ = ( +g ` G ) |
||
| Assertion | zlmplusg | |- .+ = ( +g ` W ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zlmbas.w | |- W = ( ZMod ` G ) |
|
| 2 | zlmplusg.2 | |- .+ = ( +g ` G ) |
|
| 3 | plusgid | |- +g = Slot ( +g ` ndx ) |
|
| 4 | scandxnplusgndx | |- ( Scalar ` ndx ) =/= ( +g ` ndx ) |
|
| 5 | 4 | necomi | |- ( +g ` ndx ) =/= ( Scalar ` ndx ) |
| 6 | vscandxnplusgndx | |- ( .s ` ndx ) =/= ( +g ` ndx ) |
|
| 7 | 6 | necomi | |- ( +g ` ndx ) =/= ( .s ` ndx ) |
| 8 | 1 3 5 7 | zlmlem | |- ( +g ` G ) = ( +g ` W ) |
| 9 | 2 8 | eqtri | |- .+ = ( +g ` W ) |