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grothendieck_universe [2014/12/07 22:33] nikolaj |
grothendieck_universe [2014/12/07 22:33] nikolaj |
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| >I reverse-engineered this from the metamath page, so it needs to be checked. | >I reverse-engineered this from the metamath page, so it needs to be checked. | ||
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| $Y\ {\approx}\ {\mathfrak G}\equiv\exists f. \forall x.\left((x \in Y) \implies \exists!u.\ \{x, u\} \in f\right) \land \left((x \in {\mathfrak G}\setminus Y) \implies \exists(y \in Y).\ \{y,x\} \in f\right)$ | $Y\ {\approx}\ {\mathfrak G}\equiv\exists f. \forall x.\left((x \in Y) \implies \exists!u.\ \{x, u\} \in f\right) \land \left((x \in {\mathfrak G}\setminus Y) \implies \exists(y \in Y).\ \{y,x\} \in f\right)$ | ||
