fi1: B → A
}.
-interpretation "logical iff" 'iff x y = (Iff x y).
-
notation "hvbox(a break ⇔ b)" right associative with precedence 25 for @{'iff1 $a $b}.
+interpretation "logical iff" 'iff x y = (Iff x y).
interpretation "logical iff type1" 'iff1 x y = (Iff1 x y).
inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
ex_introT: ∀w:A. P w → exT A P.
-
-notation "\ll term 19 a, break term 19 b \gg"
-with precedence 90 for @{'dependent_pair $a $b}.
-interpretation "dependent pair" 'dependent_pair a b =
- (ex_introT _ _ a b).
interpretation "CProp exists" 'exists \eta.x = (exT _ x).
interpretation "constructive not" 'not x = (Not x).
-definition cotransitive ≝
+definition cotransitive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
λC:Type0.λlt:C→C→CProp0.∀x,y,z:C. lt x y → lt x z ∨ lt z y.
-definition coreflexive ≝ λC:Type0.λlt:C→C→CProp0. ∀x:C. ¬ (lt x x).
+definition coreflexive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
+ λC:Type0.λlt:C→C→CProp0. ∀x:C. ¬ (lt x x).
-definition symmetric ≝ λC:Type0.λlt:C→C→CProp0. ∀x,y:C.lt x y → lt y x.
+definition symmetric: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝
+ λC:Type0.λlt:C→C→CProp0. ∀x,y:C.lt x y → lt y x.
-definition antisymmetric ≝ λA:Type0.λR:A→A→CProp0.λeq:A→A→Prop.∀x:A.∀y:A.R x y→R y x→eq x y.
+definition antisymmetric: ∀A:Type0. ∀R:A→A→CProp0. ∀eq:A→A→Prop.CProp0 ≝
+ λA:Type0.λR:A→A→CProp0.λeq:A→A→Prop.∀x:A.∀y:A.R x y→R y x→eq x y.
-definition reflexive ≝ λA:Type0.λR:A→A→CProp0.∀x:A.R x x.
+definition reflexive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x:A.R x x.
-definition transitive ≝ λA:Type0.λR:A→A→CProp0.∀x,y,z:A.R x y → R y z → R x z.
-
+definition transitive: ∀C:Type0. ∀lt:C→C→CProp0.CProp0 ≝ λA:Type0.λR:A→A→CProp0.∀x,y,z:A.R x y → R y z → R x z.
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