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217 lemma card_bij: |
217 lemma card_bij: |
218 "[|f \<in> A\<rightarrow>B; inj_on f A; |
218 "[|f \<in> A\<rightarrow>B; inj_on f A; |
219 g \<in> B\<rightarrow>A; inj_on g B; finite A; finite B|] ==> card(A) = card(B)" |
219 g \<in> B\<rightarrow>A; inj_on g B; finite A; finite B|] ==> card(A) = card(B)" |
220 by (blast intro: card_inj order_antisym) |
220 by (blast intro: card_inj order_antisym) |
221 |
221 |
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222 |
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223 (*The following declarations generate polymorphic Skolem functions for |
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224 these theorems. Eventually they should become redundant, once this |
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225 is done automatically.*) |
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226 |
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227 declare FuncSet.Pi_I [skolem] |
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228 declare FuncSet.Pi_mono [skolem] |
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229 declare FuncSet.extensionalityI [skolem] |
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230 declare FuncSet.funcsetI [skolem] |
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231 declare FuncSet.restrictI [skolem] |
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232 declare FuncSet.restrict_in_funcset [skolem] |
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233 |
222 end |
234 end |