add 'Proof Using' hints to enable -quick compilation

theories/lifetime/primitive.v

@@ -3,6 +3,7 @@ From iris.algebra Require Import csum auth frac gmap agree gset.
 From iris.base_logic Require Import big_op.
 From iris.base_logic.lib Require Import boxes fractional.
 From iris.proofmode Require Import tactics.
+Set Default Proof Using "Type".
 Import uPred.
 
 Section primitive.

theories/lifetime/raw_reborrow.v

@@ -4,6 +4,7 @@ From iris.algebra Require Import csum auth frac gmap agree gset.
 From iris.base_logic Require Import big_op.
 From iris.base_logic.lib Require Import boxes.
 From iris.proofmode Require Import tactics.
+Set Default Proof Using "Type".
 
 Section rebor.
 Context `{invG Σ, lftG Σ}.

theories/lifetime/reborrow.v

@@ -4,6 +4,7 @@ From iris.algebra Require Import csum auth frac gmap agree gset.
 From iris.base_logic Require Import big_op.
 From iris.base_logic.lib Require Import boxes.
 From iris.proofmode Require Import tactics.
+Set Default Proof Using "Type".
 
 Section reborrow.
 Context `{invG Σ, lftG Σ}.

theories/lifetime/shr_borrow.v

 From iris.algebra Require Import gmap auth frac.
 From iris.proofmode Require Import tactics.
 From lrust.lifetime Require Export derived.
+Set Default Proof Using "Type".
 
 (** Shared bors  *)
 Definition shr_bor `{invG Σ, lftG Σ} κ (P : iProp Σ) :=

theories/typing/bool.v

@@ -2,6 +2,7 @@ From iris.base_logic Require Import big_op.
 From iris.proofmode Require Import tactics.
 From lrust.typing Require Export type.
 From lrust.typing Require Import programs.
+Set Default Proof Using "Type".
 
 Section bool.
   Context `{typeG Σ}.

theories/typing/borrow.v

@@ -4,6 +4,7 @@ From lrust.lifetime Require Import reborrow frac_borrow.
 From lrust.lang Require Import heap.
 From lrust.typing Require Export uniq_bor shr_bor own.
 From lrust.typing Require Import lft_contexts type_context programs.
+Set Default Proof Using "Type".
 
 (** The rules for borrowing and derferencing borrowed non-Copy pointers are in
   a separate file so make sure that own.v and uniq_bor.v can be compiled

theories/typing/cont.v

@@ -3,6 +3,7 @@ From iris.proofmode Require Import tactics.
 From lrust.lifetime Require Import borrow.
 From lrust.typing Require Export type.
 From lrust.typing Require Import programs.
+Set Default Proof Using "Type".
 
 Section typing.
   Context `{typeG Σ}.

theories/typing/cont_context.v

@@ -3,6 +3,7 @@ From iris.base_logic Require Import big_op.
 From lrust.lang Require Import notation.
 From lrust.lifetime Require Import definitions.
 From lrust.typing Require Import type lft_contexts type_context.
+Set Default Proof Using "Type".
 
 Section cont_context_def.
   Context `{typeG Σ}.

theories/typing/fixpoint.v

 From lrust.lifetime Require Import definitions.
 From lrust.typing Require Export lft_contexts type bool.
+Set Default Proof Using "Type".
 
 Section fixpoint.
   Context `{typeG Σ}.

theories/typing/function.v

@@ -4,6 +4,7 @@ From iris.algebra Require Import vector.
 From lrust.lifetime Require Import borrow.
 From lrust.typing Require Export type.
 From lrust.typing Require Import programs cont.
+Set Default Proof Using "Type".
 
 Section fn.
   Context `{typeG Σ} {A : Type} {n : nat}.

theories/typing/int.v

 From iris.proofmode Require Import tactics.
 From lrust.typing Require Export type.
 From lrust.typing Require Import bool programs.
+Set Default Proof Using "Type".
 
 Section int.
   Context `{typeG Σ}.

theories/typing/lft_contexts.v

@@ -2,6 +2,7 @@ From iris.proofmode Require Import tactics.
 From iris.base_logic Require Import big_op.
 From iris.base_logic.lib Require Import fractional.
 From lrust.lifetime Require Import derived borrow frac_borrow.
+Set Default Proof Using "Type".
 
 Inductive elctx_elt : Type :=
 | ELCtx_Alive (κ : lft)

theories/typing/own.v

@@ -6,6 +6,7 @@ From lrust.lang Require Export new_delete.
 From lrust.lang Require Import memcpy.
 From lrust.typing Require Export type.
 From lrust.typing Require Import uninit type_context programs.
+Set Default Proof Using "Type".
 
 Section own.
   Context `{typeG Σ}.

theories/typing/product.v

@@ -2,6 +2,7 @@ From iris.proofmode Require Import tactics.
 From iris.algebra Require Import list.
 From lrust.lifetime Require Import borrow frac_borrow.
 From lrust.typing Require Export type.
+Set Default Proof Using "Type".
 
 Section product.
   Context `{typeG Σ}.

theories/typing/product_split.v

@@ -4,6 +4,7 @@ From iris.base_logic Require Import big_op.
 From lrust.lifetime Require Import borrow frac_borrow.
 From lrust.typing Require Export type.
 From lrust.typing Require Import type_context lft_contexts product own uniq_bor shr_bor.
+Set Default Proof Using "Type".
 
 Section product_split.
   Context `{typeG Σ}.

theories/typing/programs.v

@@ -3,6 +3,7 @@ From lrust.lang Require Export notation.
 From lrust.lang Require Import proofmode memcpy.
 From lrust.lifetime Require Import frac_borrow reborrow borrow creation.
 From lrust.typing Require Export type lft_contexts type_context cont_context.
+Set Default Proof Using "Type".
 
 Section typing.
   Context `{typeG Σ}.

theories/typing/shr_bor.v

@@ -3,6 +3,7 @@ From iris.proofmode Require Import tactics.
 From lrust.lifetime Require Import frac_borrow.
 From lrust.typing Require Export type.
 From lrust.typing Require Import lft_contexts type_context programs.
+Set Default Proof Using "Type".
 
 Section shr_bor.
   Context `{typeG Σ}.

theories/typing/sum.v

@@ -3,6 +3,7 @@ From iris.algebra Require Import list.
 From iris.base_logic Require Import fractional.
 From lrust.lifetime Require Import borrow frac_borrow.
 From lrust.typing Require Export type.
+Set Default Proof Using "Type".
 
 Section sum.
   Context `{typeG Σ}.

theories/typing/tests/get_x.v

@@ -2,6 +2,7 @@ From lrust.lifetime Require Import definitions.
 From lrust.lang Require Import new_delete.
 From lrust.typing Require Import programs product product_split own uniq_bor
                     shr_bor int function lft_contexts uninit cont.
+Set Default Proof Using "Type".
 
 Section get_x.
   Context `{typeG Σ}.

theories/typing/type.v

@@ -3,6 +3,7 @@ From iris.base_logic Require Import big_op.
 From lrust.lang Require Export proofmode notation.
 From lrust.lifetime Require Import borrow frac_borrow reborrow.
 From lrust.typing Require Import lft_contexts.
+Set Default Proof Using "Type".
 
 Class typeG Σ := TypeG {
   type_heapG :> heapG Σ;