equal
deleted
inserted
replaced
159 qed |
159 qed |
160 |
160 |
161 end |
161 end |
162 |
162 |
163 lemma Sup_image_mono_le: |
163 lemma Sup_image_mono_le: |
164 fixes le_b (infix "\<sqsubseteq>" 60) and Sup_b ("\<Or> _" [900] 900) |
164 fixes le_b (infix "\<sqsubseteq>" 60) and Sup_b ("\<Or>") |
165 assumes ccpo: "class.ccpo Sup_b (\<sqsubseteq>) lt_b" |
165 assumes ccpo: "class.ccpo Sup_b (\<sqsubseteq>) lt_b" |
166 assumes chain: "Complete_Partial_Order.chain (\<sqsubseteq>) Y" |
166 assumes chain: "Complete_Partial_Order.chain (\<sqsubseteq>) Y" |
167 and mono: "\<And>x y. \<lbrakk> x \<sqsubseteq> y; x \<in> Y \<rbrakk> \<Longrightarrow> f x \<le> f y" |
167 and mono: "\<And>x y. \<lbrakk> x \<sqsubseteq> y; x \<in> Y \<rbrakk> \<Longrightarrow> f x \<le> f y" |
168 shows "Sup (f ` Y) \<le> f (\<Or>Y)" |
168 shows "Sup (f ` Y) \<le> f (\<Or>Y)" |
169 proof(rule ccpo_Sup_least) |
169 proof(rule ccpo_Sup_least) |