interpretation "constructive or" 'or x y = (Or x y).
+inductive Or3 (A,B,C:CProp) : CProp ≝
+ | Left3 : A → Or3 A B C
+ | Middle3 : B → Or3 A B C
+ | Right3 : C → Or3 A B C.
+
+interpretation "constructive ternary or" 'or3 x y z= (Or3 x y z).
+
+notation < "hvbox(a break ∨ b break ∨ c)" with precedence 35 for @{'or3 $a $b $c}.
+
+inductive Or4 (A,B,C,D:CProp) : CProp ≝
+ | Left3 : A → Or4 A B C D
+ | Middle3 : B → Or4 A B C D
+ | Right3 : C → Or4 A B C D
+ | Extra3: D → Or4 A B C D.
+
+interpretation "constructive ternary or" 'or4 x y z t = (Or4 x y z t).
+
+notation < "hvbox(a break ∨ b break ∨ c break ∨ d)" with precedence 35 for @{'or4 $a $b $c $d}.
+
inductive And (A,B:CProp) : CProp ≝
| Conj : A → B → And A B.
inductive And3 (A,B,C:CProp) : CProp ≝
| Conj3 : A → B → C → And3 A B C.
-notation < "a ∧ b ∧ c" with precedence 35 for @{'and3 $a $b $c}.
+notation < "hvbox(a break ∧ b break ∧ c)" with precedence 35 for @{'and3 $a $b $c}.
-interpretation "constructive ternary and" 'and3 x y z = (Conj3 x y z).
+interpretation "constructive ternary and" 'and3 x y z = (And3 x y z).
inductive And4 (A,B,C,D:CProp) : CProp ≝
| Conj4 : A → B → C → D → And4 A B C D.
-notation < "a ∧ b ∧ c ∧ d" with precedence 35 for @{'and4 $a $b $c $d}.
+notation < "hvbox(a break ∧ b break ∧ c break ∧ d)" with precedence 35 for @{'and4 $a $b $c $d}.
-interpretation "constructive quaternary and" 'and4 x y z t = (Conj4 x y z t).
+interpretation "constructive quaternary and" 'and4 x y z t = (And4 x y z t).
inductive exT (A:Type) (P:A→CProp) : CProp ≝
ex_introT: ∀w:A. P w → exT A P.
definition reflexive ≝ λA:Type.λR:A→A→CProp.∀x:A.R x x.
definition transitive ≝ λA:Type.λR:A→A→CProp.∀x,y,z:A.R x y → R y z → R x z.
+