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successor_set [2014/03/21 11:11] 127.0.0.1 external edit |
successor_set [2014/03/27 10:58] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $X$ | | | @#55CCEE: context | @#55CCEE: $X$ | | ||
| - | |||
| | @#FFBB00: definiendum | @#FFBB00: $ S(X) \equiv X \cup \{X\} $ | | | @#FFBB00: definiendum | @#FFBB00: $ S(X) \equiv X \cup \{X\} $ | | ||
| Line 8: | Line 7: | ||
| === Theorems === | === Theorems === | ||
| ^ $ X\in S(X) $ ^ | ^ $ X\in S(X) $ ^ | ||
| - | ^ $ (S(X)=S(Y))\implies (X=Y) $ ^ | + | ^ $ (S(X)=S(Y))\Rightarrow (X=Y) $ ^ |
| - | ^ $ (Y\in S(X))\iff (Y=X\lor Y=\{X\}) $ ^ | + | ^ $ (Y\in S(X))\Leftrightarrow (Y=X\lor Y=\{X\}) $ ^ |
| ^ $ X\neq S(X) $ ^ | ^ $ X\neq S(X) $ ^ | ||
| === Reference === | === Reference === | ||
| Line 16: | Line 15: | ||
| ProofWiki: [[http://www.proofwiki.org/wiki/Definition:Successor_Set|Successor set]] | ProofWiki: [[http://www.proofwiki.org/wiki/Definition:Successor_Set|Successor set]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Context === | + | === Requirements === |
| [[Singleton]], [[Union]] | [[Singleton]], [[Union]] | ||
