| context | $\langle F,+,*\rangle \in \mathrm{field}(F) $ |
| definiendum | $\langle \hat F,\hat +,\hat*\rangle\in\mathrm{subfield}(\langle F,+,*\rangle) $ |
| postulate | $ 0,1\in \hat F $ |
| $x,y\in \hat F$ |
| postulate | $ x+y,\ x*y,\ x-y,\ x*y^{-1}\in \hat F $ |
| postulate | $ x\ \hat +\ y,\ x\ \hat *\ y,\ x\ \hat -\ y,\ x*y^{\hat{-1}} \in \hat F $ |
Wikipedia: Field