equal
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replaced
324 lemma bin_chain: "x \<sqsubseteq> y \<Longrightarrow> chain (\<lambda>i. if i=0 then x else y)" |
324 lemma bin_chain: "x \<sqsubseteq> y \<Longrightarrow> chain (\<lambda>i. if i=0 then x else y)" |
325 by (rule chainI, simp) |
325 by (rule chainI, simp) |
326 |
326 |
327 lemma bin_chainmax: |
327 lemma bin_chainmax: |
328 "x \<sqsubseteq> y \<Longrightarrow> max_in_chain (Suc 0) (\<lambda>i. if i=0 then x else y)" |
328 "x \<sqsubseteq> y \<Longrightarrow> max_in_chain (Suc 0) (\<lambda>i. if i=0 then x else y)" |
329 by (unfold max_in_chain_def, simp) |
329 unfolding max_in_chain_def by simp |
330 |
330 |
331 lemma lub_bin_chain: |
331 lemma lub_bin_chain: |
332 "x \<sqsubseteq> y \<Longrightarrow> range (\<lambda>i::nat. if i=0 then x else y) <<| y" |
332 "x \<sqsubseteq> y \<Longrightarrow> range (\<lambda>i::nat. if i=0 then x else y) <<| y" |
333 apply (frule bin_chain) |
333 apply (frule bin_chain) |
334 apply (drule bin_chainmax) |
334 apply (drule bin_chainmax) |