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207 lemma card_bij: |
207 lemma card_bij: |
208 "[|f \<in> A\<rightarrow>B; inj_on f A; |
208 "[|f \<in> A\<rightarrow>B; inj_on f A; |
209 g \<in> B\<rightarrow>A; inj_on g B; finite A; finite B|] ==> card(A) = card(B)" |
209 g \<in> B\<rightarrow>A; inj_on g B; finite A; finite B|] ==> card(A) = card(B)" |
210 by (blast intro: card_inj order_antisym) |
210 by (blast intro: card_inj order_antisym) |
211 |
211 |
212 |
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213 (*The following declarations generate polymorphic Skolem functions for |
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214 these theorems. Eventually they should become redundant, once this |
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215 is done automatically.*) |
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216 |
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217 declare FuncSet.Pi_I [skolem] |
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218 declare FuncSet.Pi_mono [skolem] |
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219 declare FuncSet.extensionalityI [skolem] |
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220 declare FuncSet.funcsetI [skolem] |
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221 declare FuncSet.restrictI [skolem] |
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222 declare FuncSet.restrict_in_funcset [skolem] |
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223 |
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224 end |
212 end |