diff --git a/theories/base.v b/theories/base.v
index 51dcdad2f233e0fa907ac48a321b8dd648e4044d..859c6f009c545ee34b790e35bda610872105c3d9 100644
--- a/theories/base.v
+++ b/theories/base.v
@@ -9,6 +9,7 @@ Global Set Automatic Coercions Import.
 Global Set Asymmetric Patterns.
 Global Unset Transparent Obligations.
 From Coq Require Export Morphisms RelationClasses List Bool Utf8 Setoid.
+Set Default Proof Using "Type*".
 Export ListNotations.
 From Coq.Program Require Export Basics Syntax.
 Obligation Tactic := idtac.
diff --git a/theories/bset.v b/theories/bset.v
index 9c8fe4753c8c47a3a3eda31e1693ef2521f5429c..91501e33703fdda2297814a3d9f5ea63124cf7d9 100644
--- a/theories/bset.v
+++ b/theories/bset.v
@@ -2,6 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements bsets as functions into Prop. *)
 From stdpp Require Export prelude.
+Set Default Proof Using "Type*".
 
 Record bset (A : Type) : Type := mkBSet { bset_car : A → bool }.
 Arguments mkBSet {_} _.
diff --git a/theories/coPset.v b/theories/coPset.v
index c1212ffd1d8fc5abd16ce2a627115f2bcbaf401e..49e323349baf4cb6a68ec7123834a6a5fe16e337 100644
--- a/theories/coPset.v
+++ b/theories/coPset.v
@@ -13,6 +13,7 @@ Since [positive]s are bitstrings, we encode [coPset]s as trees that correspond
 to the decision function that map bitstrings to bools. *)
 From stdpp Require Export collections.
 From stdpp Require Import pmap gmap mapset.
+Set Default Proof Using "Type*".
 Local Open Scope positive_scope.
 
 (** * The tree data structure *)
diff --git a/theories/collections.v b/theories/collections.v
index 126dc59e1ea18bbf692c658facd74c651da09160..672eac8c8c208092ef2e31727dadc150a79cc6e9 100644
--- a/theories/collections.v
+++ b/theories/collections.v
@@ -4,6 +4,7 @@
 importantly, it implements some tactics to automatically solve goals involving
 collections. *)
 From stdpp Require Export orders list.
+Set Default Proof Using "Type*".
 
 Instance collection_equiv `{ElemOf A C} : Equiv C := λ X Y,
   ∀ x, x ∈ X ↔ x ∈ Y.
diff --git a/theories/countable.v b/theories/countable.v
index 00e84a9eace9ba34d950be6b6b002791733d8687..aa7dad648869048d62f144a4b52af7922ec4b758 100644
--- a/theories/countable.v
+++ b/theories/countable.v
@@ -1,6 +1,7 @@
 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 From stdpp Require Export list.
+Set Default Proof Using "Type*".
 Local Open Scope positive.
 
 Class Countable A `{EqDecision A} := {
diff --git a/theories/decidable.v b/theories/decidable.v
index 4748a82201b7922bbf347084767bc86003bc085b..57dc031f3a62f74df47f68f9dcc6032070f33fa8 100644
--- a/theories/decidable.v
+++ b/theories/decidable.v
@@ -4,6 +4,7 @@
 with a decidable equality. Such propositions are collected by the [Decision]
 type class. *)
 From stdpp Require Export proof_irrel.
+Set Default Proof Using "Type*".
 
 Hint Extern 200 (Decision _) => progress (lazy beta) : typeclass_instances.
 
diff --git a/theories/fin_collections.v b/theories/fin_collections.v
index ed094d36eb2b7aa8599d03e60e3b3aab891ab775..fd7a4d38ea2ce08041a439e7d68288e2c4f71cce 100644
--- a/theories/fin_collections.v
+++ b/theories/fin_collections.v
@@ -6,6 +6,7 @@ principles on finite collections . *)
 From Coq Require Import Permutation.
 From stdpp Require Import relations listset.
 From stdpp Require Export numbers collections.
+Set Default Proof Using "Type*".
 
 Instance collection_size `{Elements A C} : Size C := length ∘ elements.
 Definition collection_fold `{Elements A C} {B}
diff --git a/theories/fin_map_dom.v b/theories/fin_map_dom.v
index 5856b682d344e88cbb409c0c9e5d4334cf9f727d..cbc6c1a1015b601cf87f18fc5ced9811e58ed91e 100644
--- a/theories/fin_map_dom.v
+++ b/theories/fin_map_dom.v
@@ -4,6 +4,7 @@
 maps. We provide such an axiomatization, instead of implementing the domain
 function in a generic way, to allow more efficient implementations. *)
 From stdpp Require Export collections fin_maps.
+Set Default Proof Using "Type*".
 
 Class FinMapDom K M D `{FMap M,
     ∀ A, Lookup K A (M A), ∀ A, Empty (M A), ∀ A, PartialAlter K A (M A),
diff --git a/theories/fin_maps.v b/theories/fin_maps.v
index 2c8634da993b7667842c6fa07f753f6a9db829d0..cc85921f2f41792e5d4c8f6dd0b91d3d968f6764 100644
--- a/theories/fin_maps.v
+++ b/theories/fin_maps.v
@@ -6,6 +6,7 @@ induction principles for finite maps and implements the tactic
 [simplify_map_eq] to simplify goals involving finite maps. *)
 From Coq Require Import Permutation.
 From stdpp Require Export relations orders vector.
+Set Default Proof Using "Type*".
 
 (** * Axiomatization of finite maps *)
 (** We require Leibniz equality to be extensional on finite maps. This of
diff --git a/theories/finite.v b/theories/finite.v
index eb8b868eec3e4188c48c13adaa7ffdc92a2f73a3..d15fa39e85ad3aabfef227b1384c56f309aec63f 100644
--- a/theories/finite.v
+++ b/theories/finite.v
@@ -1,6 +1,7 @@
 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 From stdpp Require Export countable vector.
+Set Default Proof Using "Type*".
 
 Class Finite A `{EqDecision A} := {
   enum : list A;
diff --git a/theories/functions.v b/theories/functions.v
index 44da98377fcf8b828a7de9743ecb462ad47df188..4c37187d2a8146e1bb0dacd986d8ffab3a0b50f8 100644
--- a/theories/functions.v
+++ b/theories/functions.v
@@ -1,4 +1,5 @@
 From stdpp Require Export base tactics.
+Set Default Proof Using "Type*".
 
 Section definitions.
   Context {A T : Type} `{EqDecision A}.
diff --git a/theories/gmap.v b/theories/gmap.v
index 3f4c395836b916d21cf58cb4ca4f987c20288cd9..a1bf157f471bca4c9c295a82c720bbbaa68d94a2 100644
--- a/theories/gmap.v
+++ b/theories/gmap.v
@@ -4,6 +4,7 @@
 type. The implementation is based on [Pmap]s, radix-2 search trees. *)
 From stdpp Require Export countable fin_maps fin_map_dom.
 From stdpp Require Import pmap mapset set.
+Set Default Proof Using "Type*".
 
 (** * The data structure *)
 (** We pack a [Pmap] together with a proof that ensures that all keys correspond
diff --git a/theories/gmultiset.v b/theories/gmultiset.v
index 2c9f85356f587d24d268df36167eb3b3e633214c..7f1f83eb762e96661a72fd215a1bc8f52f142abe 100644
--- a/theories/gmultiset.v
+++ b/theories/gmultiset.v
@@ -1,6 +1,7 @@
 (* Copyright (c) 2012-2016, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 From stdpp Require Import gmap.
+Set Default Proof Using "Type*".
 
 Record gmultiset A `{Countable A} := GMultiSet { gmultiset_car : gmap A nat }.
 Arguments GMultiSet {_ _ _} _.
diff --git a/theories/hashset.v b/theories/hashset.v
index e93e5214f50507a1debfe6dd72f6c52e0b3a51c4..ffed2bd15a4a66b36bbd27d1ddce94f93d57be80 100644
--- a/theories/hashset.v
+++ b/theories/hashset.v
@@ -5,6 +5,7 @@ using radix-2 search trees. Each hash bucket is thus indexed using an binary
 integer of type [Z], and contains an unordered list without duplicates. *)
 From stdpp Require Export fin_maps listset.
 From stdpp Require Import zmap.
+Set Default Proof Using "Type*".
 
 Record hashset {A} (hash : A → Z) := Hashset {
   hashset_car : Zmap (list A);
diff --git a/theories/hlist.v b/theories/hlist.v
index 6f4c5227b7b1d9468d3791bbcd9e965fd9825ce5..39ad98053bf35cf7dd8ca1633b567eb5b0c53134 100644
--- a/theories/hlist.v
+++ b/theories/hlist.v
@@ -1,4 +1,5 @@
 From stdpp Require Import tactics.
+Set Default Proof Using "Type*".
 Local Set Universe Polymorphism.
 
 (* Not using [list Type] in order to avoid universe inconsistencies *)
diff --git a/theories/lexico.v b/theories/lexico.v
index 42d6b31903ead119b0a1ebfc444a9c700707ab68..f5402ebd63331014aecad124d372c68d0ffe73d7 100644
--- a/theories/lexico.v
+++ b/theories/lexico.v
@@ -3,6 +3,7 @@
 (** This files defines a lexicographic order on various common data structures
 and proves that it is a partial order having a strong variant of trichotomy. *)
 From stdpp Require Import numbers.
+Set Default Proof Using "Type*".
 
 Notation cast_trichotomy T :=
   match T with
diff --git a/theories/list.v b/theories/list.v
index 5847a12428d30fca31c48ecfadca66a0834d862d..a9f260c4432ac29dbc0000b70d2ba8019ae285d5 100644
--- a/theories/list.v
+++ b/theories/list.v
@@ -4,6 +4,7 @@
 are not in the Coq standard library. *)
 From Coq Require Export Permutation.
 From stdpp Require Export numbers base option.
+Set Default Proof Using "Type*".
 
 Arguments length {_} _.
 Arguments cons {_} _ _.
diff --git a/theories/listset.v b/theories/listset.v
index 8ba410eaa1b1b48eca1f35b7aebc83cee8955438..8966cc2e86df5251be0505163e81bdb8e1b3dd77 100644
--- a/theories/listset.v
+++ b/theories/listset.v
@@ -3,6 +3,7 @@
 (** This file implements finite set as unordered lists without duplicates
 removed. This implementation forms a monad. *)
 From stdpp Require Export collections list.
+Set Default Proof Using "Type*".
 
 Record listset A := Listset { listset_car: list A }.
 Arguments listset_car {_} _.
diff --git a/theories/listset_nodup.v b/theories/listset_nodup.v
index 73447c3519fd31ceae7421cac4ef63ae31498f07..e3b76d511b0bc4854471608d97d07dca6f08e2b2 100644
--- a/theories/listset_nodup.v
+++ b/theories/listset_nodup.v
@@ -4,6 +4,7 @@
 Although this implementation is slow, it is very useful as decidable equality
 is the only constraint on the carrier set. *)
 From stdpp Require Export collections list.
+Set Default Proof Using "Type*".
 
 Record listset_nodup A := ListsetNoDup {
   listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car
diff --git a/theories/mapset.v b/theories/mapset.v
index ffaae8b4afd4e0b9204d05d0c9bd9dcf4efc19b7..1e921468a848f350ce99cf263fb6bcf12ae544bc 100644
--- a/theories/mapset.v
+++ b/theories/mapset.v
@@ -4,6 +4,7 @@
 elements of the unit type. Since maps enjoy extensional equality, the
 constructed finite sets do so as well. *)
 From stdpp Require Export fin_map_dom.
+(* FIXME: This file needs a 'Proof Using' hint. *)
 
 Record mapset (M : Type → Type) : Type :=
   Mapset { mapset_car: M (unit : Type) }.
diff --git a/theories/natmap.v b/theories/natmap.v
index 0cd0a4c3c57f071d165fd6120e3cff4f4ff26745..d109590bbc65a0980f430860139a51b2db69f72a 100644
--- a/theories/natmap.v
+++ b/theories/natmap.v
@@ -4,6 +4,7 @@
 over Coq's data type of unary natural numbers [nat]. The implementation equips
 a list with a proof of canonicity. *)
 From stdpp Require Import fin_maps mapset.
+Set Default Proof Using "Type*".
 
 Notation natmap_raw A := (list (option A)).
 Definition natmap_wf {A} (l : natmap_raw A) :=
diff --git a/theories/nmap.v b/theories/nmap.v
index 00c249b0996ee21b6140da250054e85df05c5994..12645efbaa269de49be4cc9c195d25001a6a5c5f 100644
--- a/theories/nmap.v
+++ b/theories/nmap.v
@@ -4,6 +4,7 @@
 maps whose keys range over Coq's data type of binary naturals [N]. *)
 From stdpp Require Import pmap mapset.
 From stdpp Require Export prelude fin_maps.
+Set Default Proof Using "Type*".
 
 Local Open Scope N_scope.
 
diff --git a/theories/numbers.v b/theories/numbers.v
index 38f5a86217647cb76f7d8d982041d359a4019c32..034a4ca14ce014e8e918fadf55eb19fdf28752d1 100644
--- a/theories/numbers.v
+++ b/theories/numbers.v
@@ -6,6 +6,7 @@ notations. *)
 From Coq Require Export EqdepFacts PArith NArith ZArith NPeano.
 From Coq Require Import QArith Qcanon.
 From stdpp Require Export base decidable option.
+Set Default Proof Using "Type*".
 Open Scope nat_scope.
 
 Coercion Z.of_nat : nat >-> Z.
diff --git a/theories/option.v b/theories/option.v
index 73ae6eff1f69195554bac488c2b11b3e9d6bac4d..63378a36a1136b056b363daadcf614a88c4ed9bf 100644
--- a/theories/option.v
+++ b/theories/option.v
@@ -3,6 +3,7 @@
 (** This file collects general purpose definitions and theorems on the option
 data type that are not in the Coq standard library. *)
 From stdpp Require Export tactics.
+Set Default Proof Using "Type*".
 
 Inductive option_reflect {A} (P : A → Prop) (Q : Prop) : option A → Type :=
   | ReflectSome x : P x → option_reflect P Q (Some x)
diff --git a/theories/orders.v b/theories/orders.v
index b0d84aeb1d297b30658a1935502e4a5a791d424f..bc301900b0f68d31fe893caaaba650a2e11194e6 100644
--- a/theories/orders.v
+++ b/theories/orders.v
@@ -3,6 +3,7 @@
 (** Properties about arbitrary pre-, partial, and total orders. We do not use
 the relation [⊆] because we often have multiple orders on the same structure *)
 From stdpp Require Export tactics.
+Set Default Proof Using "Type*".
 
 Section orders.
   Context {A} {R : relation A}.
diff --git a/theories/pmap.v b/theories/pmap.v
index 8237bdccef4cbdedff419336230c5459817dd990..a6966f39ef92ad83321ac192ca5704a3e310fafc 100644
--- a/theories/pmap.v
+++ b/theories/pmap.v
@@ -10,6 +10,7 @@ Leibniz equality to become extensional. *)
 From Coq Require Import PArith.
 From stdpp Require Import mapset countable.
 From stdpp Require Export fin_maps.
+Set Default Proof Using "Type*".
 
 Local Open Scope positive_scope.
 Local Hint Extern 0 (@eq positive _ _) => congruence.
diff --git a/theories/pretty.v b/theories/pretty.v
index 58fd38347cb830e869560976e93956b39a6fa73f..afd2b6899b6b6f2925c00aa6a49d34f92450315d 100644
--- a/theories/pretty.v
+++ b/theories/pretty.v
@@ -3,6 +3,7 @@
 From stdpp Require Export strings.
 From stdpp Require Import relations.
 From Coq Require Import Ascii.
+Set Default Proof Using "Type*".
 
 Class Pretty A := pretty : A → string.
 Definition pretty_N_char (x : N) : ascii :=
diff --git a/theories/proof_irrel.v b/theories/proof_irrel.v
index 2af33406524bb5cc3d32589f5c6c838e88cb2b76..4d9c6d7d83bf459912342375e766e2b18dde9d97 100644
--- a/theories/proof_irrel.v
+++ b/theories/proof_irrel.v
@@ -2,6 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file collects facts on proof irrelevant types/propositions. *)
 From stdpp Require Export base.
+Set Default Proof Using "Type*".
 
 Hint Extern 200 (ProofIrrel _) => progress (lazy beta) : typeclass_instances.
 
diff --git a/theories/relations.v b/theories/relations.v
index dfedb109cb087a415b71c3be9113b5f6d2ecb804..3152cc7888f61f35ecc4a89339d569fdb575976c 100644
--- a/theories/relations.v
+++ b/theories/relations.v
@@ -6,6 +6,7 @@ small step semantics. This file defines a hint database [ars] containing
 some theorems on abstract rewriting systems. *)
 From Coq Require Import Wf_nat.
 From stdpp Require Export tactics base.
+Set Default Proof Using "Type*".
 
 (** * Definitions *)
 Section definitions.
diff --git a/theories/set.v b/theories/set.v
index 84ef65ff4e20fa25607515aca50d49a644563437..27a979751c390c47c7cf780e27ce6913858e6f38 100644
--- a/theories/set.v
+++ b/theories/set.v
@@ -2,6 +2,7 @@
 (* This file is distributed under the terms of the BSD license. *)
 (** This file implements sets as functions into Prop. *)
 From stdpp Require Export collections.
+Set Default Proof Using "Type*".
 
 Record set (A : Type) : Type := mkSet { set_car : A → Prop }.
 Add Printing Constructor set.
@@ -51,4 +52,4 @@ Proof. intros HPQ. constructor. apply HPQ. Qed.
 
 Global Opaque set_elem_of set_top set_empty set_singleton.
 Global Opaque set_union set_intersection set_difference.
-Global Opaque set_ret set_bind set_fmap set_join.
\ No newline at end of file
+Global Opaque set_ret set_bind set_fmap set_join.
diff --git a/theories/sorting.v b/theories/sorting.v
index 63b361831c3d7967ab4b3a2762206f427975c442..36fff7fb136f70f4645e5a4c99f4de242148e6fd 100644
--- a/theories/sorting.v
+++ b/theories/sorting.v
@@ -4,6 +4,7 @@
 standard library, but without using the module system. *)
 From Coq Require Export Sorted.
 From stdpp Require Export orders list.
+Set Default Proof Using "Type*".
 
 Section merge_sort.
   Context {A} (R : relation A) `{∀ x y, Decision (R x y)}.
diff --git a/theories/streams.v b/theories/streams.v
index 216a426b515f745754dd12667b4908c50c09c0f6..725a59158e64a09efab7bd04928ecd819535e789 100644
--- a/theories/streams.v
+++ b/theories/streams.v
@@ -1,6 +1,7 @@
 (* Copyright (c) 2012-2015, Robbert Krebbers. *)
 (* This file is distributed under the terms of the BSD license. *)
 From stdpp Require Export tactics.
+Set Default Proof Using "Type*".
 
 CoInductive stream (A : Type) : Type := scons : A → stream A → stream A.
 Arguments scons {_} _ _.
diff --git a/theories/stringmap.v b/theories/stringmap.v
index 426d392bfe0f3fa51b11f8f4d7d810f7333c61be..9de316cae7b019ad4195f5458ef3cf5d8b25a63a 100644
--- a/theories/stringmap.v
+++ b/theories/stringmap.v
@@ -6,6 +6,7 @@ search trees (uncompressed Patricia trees) as implemented in the file [pmap]
 and guarantees logarithmic-time operations. *)
 From stdpp Require Export fin_maps pretty.
 From stdpp Require Import gmap.
+Set Default Proof Using "Type*".
 
 Notation stringmap := (gmap string).
 Notation stringset := (gset string).
diff --git a/theories/strings.v b/theories/strings.v
index f08e9b0a089a8258777297e9cc70bbffa3391443..93718899c741b6b8987ec498d3406cd415cbf25f 100644
--- a/theories/strings.v
+++ b/theories/strings.v
@@ -4,6 +4,7 @@ From Coq Require Import Ascii.
 From Coq Require Export String.
 From stdpp Require Export list.
 From stdpp Require Import countable.
+Set Default Proof Using "Type*".
 
 (* To avoid randomly ending up with String.length because this module is
 imported hereditarily somewhere. *)
diff --git a/theories/tactics.v b/theories/tactics.v
index f8747a7eec416bfbcfb2cb4f85a01789748bd29c..f104f381e9c200d323e5d9a0eb578bb50ee9f8c0 100644
--- a/theories/tactics.v
+++ b/theories/tactics.v
@@ -5,6 +5,7 @@ the development. *)
 From Coq Require Import Omega.
 From Coq Require Export Lia.
 From stdpp Require Export decidable.
+Set Default Proof Using "Type*".
 
 Lemma f_equal_dep {A B} (f g : ∀ x : A, B x) x : f = g → f x = g x.
 Proof. intros ->; reflexivity. Qed.
diff --git a/theories/vector.v b/theories/vector.v
index 2d663f43cbb4bc49802946a82774970af879f1d8..b0d6d326916c6085de6d98a3b7e08407950e60c0 100644
--- a/theories/vector.v
+++ b/theories/vector.v
@@ -6,6 +6,7 @@ definitions from the standard library, but renames or changes their notations,
 so that it becomes more consistent with the naming conventions in this
 development. *)
 From stdpp Require Export list.
+Set Default Proof Using "Type*".
 Open Scope vector_scope.
 
 (** * The fin type *)
diff --git a/theories/zmap.v b/theories/zmap.v
index c3f5364722555614475136c5f9f2b653c888d19b..32689e5859a04a323fb65af130b9a75e51f293e9 100644
--- a/theories/zmap.v
+++ b/theories/zmap.v
@@ -4,6 +4,7 @@
 maps whose keys range over Coq's data type of binary naturals [Z]. *)
 From stdpp Require Import pmap mapset.
 From stdpp Require Export prelude fin_maps.
+Set Default Proof Using "Type*".
 Local Open Scope Z_scope.
 
 Record Zmap (A : Type) : Type :=