Library Coq.Logic.StrictProp

Record Box (A:SProp) : Prop := box { unbox : A }.

Inductive Squash (A:Type) : SProp := squash : A -> Squash A.

Inductive sEmpty : SProp :=.

Inductive sUnit : SProp := stt.
Definition sUnit_rect (P:sUnit -> Type) (v:P stt) (u:sUnit) : P u := v.
Definition sUnit_rec (P:sUnit -> Set) (v:P stt) (u:sUnit) : P u := v.
Definition sUnit_ind (P:sUnit -> Prop) (v:P stt) (u:sUnit) : P u := v.

Record Ssig {A:Type} (P:A->SProp) := Sexists { Spr1 : A; Spr2 : P Spr1 }.

Lemma Spr1_inj {A P} {a b : @Ssig A P} (e : Spr1 a = Spr1 b) : a = b.