src/HOL/Library/Complete_Partial_Order2.thy
changeset 69038 2ce9bc515a64
parent 68980 5717fbc55521
child 69039 51005671bee5
equal deleted inserted replaced
69037:8d8fdbc02912 69038:2ce9bc515a64
   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)