Merge PR #8817: SProp: the definitionally proof irrelevant universe

Ack-by: JasonGross
Ack-by: SkySkimmer
Reviewed-by: Zimmi48
Reviewed-by: ejgallego
Ack-by: gares
Ack-by: mattam82

2 files changed, 46 insertions, 0 deletions

diff --git a/theories/Init/Logic.v b/theories/Init/Logic.v
index b607be4f94..1a391ed799 100644
--- a/theories/Init/Logic.v
+++ b/theories/Init/Logic.v
@@ -402,6 +402,12 @@ Section Logic_lemmas.
 
   End equality.
 
+  Definition eq_sind_r :
+    forall (A:Type) (x:A) (P:A -> SProp), P x -> forall y:A, y = x -> P y.
+  Proof.
+    intros A x P H y H0. elim eq_sym with (1 := H0); assumption.
+  Defined.
+
   Definition eq_ind_r :
     forall (A:Type) (x:A) (P:A -> Prop), P x -> forall y:A, y = x -> P y.
     intros A x P H y H0. elim eq_sym with (1 := H0); assumption.
diff --git a/theories/Logic/StrictProp.v b/theories/Logic/StrictProp.v
new file mode 100644
index 0000000000..99ee54e42f
--- /dev/null
+++ b/theories/Logic/StrictProp.v
@@ -0,0 +1,40 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+(** Utilities for SProp users. *)
+
+Set Universe Polymorphism.
+Set Polymorphic Inductive Cumulativity.
+
+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.
+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.
+
+Set Primitive Projections.
+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.
+Proof.
+  destruct a,b;simpl in e.
+  destruct e. reflexivity.
+Defined.