| apply (r1 \sub\f ∘ r \sub\f)
| lapply (commute ?? r) as H;
lapply (commute ?? r1) as H1;
- apply rule (.= ASSOC1);
+ apply rule (.= ASSOC);
apply (.= #‡H1);
- apply rule (.= ASSOC1\sup -1);
+ apply rule (.= ASSOC ^ -1);
apply (.= H‡#);
- apply rule ASSOC1]
+ apply rule ASSOC]
| intros;
change with (⊩ ∘ (b\sub\c ∘ a\sub\c) = ⊩ ∘ (b'\sub\c ∘ a'\sub\c));
change in e with (⊩ ∘ a \sub\c = ⊩ ∘ a' \sub\c);
change in e1 with (⊩ ∘ b \sub\c = ⊩ ∘ b' \sub\c);
- apply rule (.= ASSOC1);
+ apply rule (.= ASSOC);
apply (.= #‡e1);
apply (.= #‡(commute ?? b'));
- apply rule (.= ASSOC1 \sup -1);
+ apply rule (.= ASSOC \sup -1);
apply (.= e‡#);
- apply rule (.= ASSOC1);
+ apply rule (.= ASSOC);
apply (.= #‡(commute ?? b')\sup -1);
- apply rule (ASSOC1 \sup -1)]
+ apply rule (ASSOC \sup -1)]
qed.
definition BP: category2.
| intros;
change with (⊩ ∘ (a34\sub\c ∘ (a23\sub\c ∘ a12\sub\c)) =
⊩ ∘ ((a34\sub\c ∘ a23\sub\c) ∘ a12\sub\c));
- apply rule (ASSOC1‡#);
+ apply rule (ASSOC‡#);
| intros;
change with (⊩ ∘ (a\sub\c ∘ (id_relation_pair o1)\sub\c) = ⊩ ∘ a\sub\c);
apply ((id_neutral_right2 ????)‡#);
interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun1 (concr _) __ (relS _) x y).
interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun1 ___ (relS _)).
-*)
\ No newline at end of file
+*)
+
+notation "□ \sub b" non associative with precedence 90 for @{'box $b}.
+notation > "□_term 90 b" non associative with precedence 90 for @{'box $b}.
+interpretation "Universal image ⊩⎻*" 'box x = (fun12 _ _ (or_f_minus_star _ _) (rel x)).
+
+notation "◊ \sub b" non associative with precedence 90 for @{'diamond $b}.
+notation > "◊_term 90 b" non associative with precedence 90 for @{'diamond $b}.
+interpretation "Existential image ⊩" 'diamond x = (fun12 _ _ (or_f _ _) (rel x)).
+
+notation "'Rest' \sub b" non associative with precedence 90 for @{'rest $b}.
+notation > "'Rest'⎽term 90 b" non associative with precedence 90 for @{'rest $b}.
+interpretation "Universal pre-image ⊩*" 'rest x = (fun12 _ _ (or_f_star _ _) (rel x)).
+
+notation "'Ext' \sub b" non associative with precedence 90 for @{'ext $b}.
+notation > "'Ext'⎽term 90 b" non associative with precedence 90 for @{'ext $b}.
+interpretation "Existential pre-image ⊩⎻" 'ext x = (fun12 _ _ (or_f_minus _ _) (rel x)).