Description: The additive law of the extended nonnegative real numbers monoid is the addition in the extended real numbers. (Contributed by Thierry Arnoux, 20-Mar-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | xrge0plusg | |- +e = ( +g ` ( RR*s |`s ( 0 [,] +oo ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ovex | |- ( 0 [,] +oo ) e. _V |
|
| 2 | eqid | |- ( RR*s |`s ( 0 [,] +oo ) ) = ( RR*s |`s ( 0 [,] +oo ) ) |
|
| 3 | xrsadd | |- +e = ( +g ` RR*s ) |
|
| 4 | 2 3 | ressplusg | |- ( ( 0 [,] +oo ) e. _V -> +e = ( +g ` ( RR*s |`s ( 0 [,] +oo ) ) ) ) |
| 5 | 1 4 | ax-mp | |- +e = ( +g ` ( RR*s |`s ( 0 [,] +oo ) ) ) |