@@ -48,11 +48,11 @@ hide_const (open) dom
4848consts dom :: "'f \<Rightarrow> 'a set"
4949
5050adhoc_overloading
51- dom Map.dom and
52- dom Relation.Domain and
53- dom Partial_Fun.pdom and
54- dom Finite_Fun.fdom and
55- dom Partial_Inj.pidom
51+ dom \<rightleftharpoons> Map.dom and
52+ dom \<rightleftharpoons> Relation.Domain and
53+ dom \<rightleftharpoons> Partial_Fun.pdom and
54+ dom \<rightleftharpoons> Finite_Fun.fdom and
55+ dom \<rightleftharpoons> Partial_Inj.pidom
5656
5757subsection \<open> Range \<close>
5858
@@ -61,11 +61,11 @@ hide_const (open) ran
6161consts ran :: "'f \<Rightarrow> 'a set"
6262
6363adhoc_overloading
64- ran Map.ran and
65- ran Relation.Range and
66- ran Partial_Fun.pran and
67- ran Finite_Fun.fran and
68- ran Partial_Inj.piran
64+ ran \<rightleftharpoons> Map.ran and
65+ ran \<rightleftharpoons> Relation.Range and
66+ ran \<rightleftharpoons> Partial_Fun.pran and
67+ ran \<rightleftharpoons> Finite_Fun.fran and
68+ ran \<rightleftharpoons> Partial_Inj.piran
6969
7070subsection \<open> Identity relation \<close>
7171
@@ -86,9 +86,9 @@ text \<open> Composition is probably the most difficult of the Z functions to im
8686consts zcomp :: "'f \<Rightarrow> 'g \<Rightarrow> 'h"
8787
8888adhoc_overloading
89- zcomp Fun.comp and
90- zcomp pfun_comp and
91- zcomp ffun_comp
89+ zcomp \<rightleftharpoons> Fun.comp and
90+ zcomp \<rightleftharpoons> pfun_comp and
91+ zcomp \<rightleftharpoons> ffun_comp
9292
9393text \<open> Once we overload @{term Fun.comp}, we need to at least have output syntax set up. \<close>
9494
@@ -109,10 +109,10 @@ consts dom_res :: "'a set \<Rightarrow> 'r \<Rightarrow> 'r" (infixr "\<Zdres>"
109109abbreviation ndres ( infixr "\<Zndres>" 85 ) where "ndres A P \<equiv> CONST dom_res (- A) P"
110110
111111adhoc_overloading
112- dom_res rel_domres
113- and dom_res pdom_res
114- and dom_res fdom_res
115- and dom_res pinj_dres
112+ dom_res \<rightleftharpoons> rel_domres
113+ and dom_res \<rightleftharpoons> pdom_res
114+ and dom_res \<rightleftharpoons> fdom_res
115+ and dom_res \<rightleftharpoons> pinj_dres
116116
117117syntax "_ndres" :: "logic \<Rightarrow> logic \<Rightarrow> logic"
118118translations "_ndres A P" == "CONST dom_res (- A) P"
@@ -124,10 +124,10 @@ consts ran_res :: "'r \<Rightarrow> 'a set \<Rightarrow> 'r" (infixl "\<Zrres>"
124124abbreviation nrres ( infixl "\<Znrres>" 86 ) where "nrres P A \<equiv> CONST ran_res P (- A)"
125125
126126adhoc_overloading
127- ran_res rel_ranres
128- and ran_res pran_res
129- and ran_res fran_res
130- and ran_res pinj_rres
127+ ran_res \<rightleftharpoons> rel_ranres
128+ and ran_res \<rightleftharpoons> pran_res
129+ and ran_res \<rightleftharpoons> fran_res
130+ and ran_res \<rightleftharpoons> pinj_rres
131131
132132subsection \<open> Relational inversion \<close>
133133
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