Description: Define multiplication on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c , and is intended to be used only by the construction. From Proposition 9-2.4 of Gleason p. 119. (Contributed by NM, 24-Aug-1995) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-mq | |- .Q = ( ( /Q o. .pQ ) |` ( Q. X. Q. ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cmq | |- .Q |
|
| 1 | cerq | |- /Q |
|
| 2 | cmpq | |- .pQ |
|
| 3 | 1 2 | ccom | |- ( /Q o. .pQ ) |
| 4 | cnq | |- Q. |
|
| 5 | 4 4 | cxp | |- ( Q. X. Q. ) |
| 6 | 3 5 | cres | |- ( ( /Q o. .pQ ) |` ( Q. X. Q. ) ) |
| 7 | 0 6 | wceq | |- .Q = ( ( /Q o. .pQ ) |` ( Q. X. Q. ) ) |