equal
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159 lemma finite_deflation_imp_deflation: |
159 lemma finite_deflation_imp_deflation: |
160 "finite_deflation d \<Longrightarrow> deflation d" |
160 "finite_deflation d \<Longrightarrow> deflation d" |
161 unfolding finite_deflation_def by simp |
161 unfolding finite_deflation_def by simp |
162 |
162 |
163 lemma finite_deflation_bottom: "finite_deflation \<bottom>" |
163 lemma finite_deflation_bottom: "finite_deflation \<bottom>" |
164 by default simp_all |
164 by standard simp_all |
165 |
165 |
166 |
166 |
167 subsection {* Continuous embedding-projection pairs *} |
167 subsection {* Continuous embedding-projection pairs *} |
168 |
168 |
169 locale ep_pair = |
169 locale ep_pair = |
356 by (fast intro: below_antisym elim: ep_pair_unique_p_lemma) |
356 by (fast intro: below_antisym elim: ep_pair_unique_p_lemma) |
357 |
357 |
358 subsection {* Composing ep-pairs *} |
358 subsection {* Composing ep-pairs *} |
359 |
359 |
360 lemma ep_pair_ID_ID: "ep_pair ID ID" |
360 lemma ep_pair_ID_ID: "ep_pair ID ID" |
361 by default simp_all |
361 by standard simp_all |
362 |
362 |
363 lemma ep_pair_comp: |
363 lemma ep_pair_comp: |
364 assumes "ep_pair e1 p1" and "ep_pair e2 p2" |
364 assumes "ep_pair e1 p1" and "ep_pair e2 p2" |
365 shows "ep_pair (e2 oo e1) (p1 oo p2)" |
365 shows "ep_pair (e2 oo e1) (p1 oo p2)" |
366 proof |
366 proof |