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181 unfolding cpow_def by (metis Card_order_Pow cardSuc_ordLess_ordLeq card_of_Card_order) |
181 unfolding cpow_def by (metis Card_order_Pow cardSuc_ordLess_ordLeq card_of_Card_order) |
182 |
182 |
183 lemma cpow_cexp_ctwo: "cpow r =o ctwo ^c r" |
183 lemma cpow_cexp_ctwo: "cpow r =o ctwo ^c r" |
184 unfolding cpow_def ctwo_def cexp_def Field_card_of by (rule card_of_Pow_Func) |
184 unfolding cpow_def ctwo_def cexp_def Field_card_of by (rule card_of_Pow_Func) |
185 |
185 |
186 |
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187 subsection {* Lists *} |
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188 |
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189 text {* |
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190 The following collection of lemmas should be seen as an user interface to the HOL theory |
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191 of cardinals. It is not expected to be complete in any sense, since its |
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192 development was driven by demand arising from the development of the (co)datatype package. |
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193 *} |
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194 |
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195 lemma clists_Cinfinite: "Cinfinite r \<Longrightarrow> clists r =o r" |
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196 unfolding cinfinite_def clists_def by (blast intro: Card_order_lists_infinite) |
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197 |
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198 lemma Card_order_clists: "Card_order (clists r)" |
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199 unfolding clists_def by (rule card_of_Card_order) |
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200 |
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201 lemma Cnotzero_clists: "Cnotzero (clists r)" |
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202 by (simp add: clists_def card_of_ordIso_czero_iff_empty lists_not_empty) |
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203 |
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204 end |
186 end |