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Inductive boolP : Prop :=
| trueP : boolP
| falseP : boolP.
Fail Check boolP_rect.
Inductive True : Prop := I : True.
Inductive False : Prop :=.
Inductive Empty_set : Set :=.
Fail Inductive Large_set : Set :=
large_constr : forall A : Set, A -> Large_set.
Inductive smallunitProp : Prop :=
| onlyProps : True -> smallunitProp.
Check smallunitProp_rect.
Inductive nonsmallunitProp : Prop :=
| notonlyProps : nat -> nonsmallunitProp.
Fail Check nonsmallunitProp_rect.
Set Printing Universes.
Inductive inferProp :=
| hasonlyProps : True -> nonsmallunitProp -> inferProp.
Check (inferProp : Prop).
Inductive inferSet :=
| hasaset : nat -> True -> nonsmallunitProp -> inferSet.
Fail Check (inferSet : Prop).
Check (inferSet : Set).
Inductive inferLargeSet :=
| hasalargeset : Set -> True -> nonsmallunitProp -> inferLargeSet.
Fail Check (inferLargeSet : Set).
Inductive largeProp : Prop := somelargeprop : Set -> largeProp.
Inductive comparison : Set :=
| Eq : comparison
| Lt : comparison
| Gt : comparison.
Inductive CompareSpecT (Peq Plt Pgt : Prop) : comparison -> Type :=
| CompEqT : Peq -> CompareSpecT Peq Plt Pgt Eq
| CompLtT : Plt -> CompareSpecT Peq Plt Pgt Lt
| CompGtT : Pgt -> CompareSpecT Peq Plt Pgt Gt.
Inductive color := Red | Black.
Inductive option (A : Type) : Type :=
| None : option A
| Some : A -> option A.
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