Library Coq.Logic.StrictProp

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

Inductive Squash (A:Type) : SProp := squash : A -> Squash A.
Arguments squash {_} _.

Inductive sEmpty : SProp :=.

Inductive sUnit : SProp := stt.

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

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