Missing fsubU1set lemma

finmap.v

@@ -147,10 +147,10 @@
 Reserved Notation "A `=P` B" (at level 70, no associativity).
 
 Reserved Notation "f @`[ key ] A" (at level 24, key at level 0).
 Reserved Notation "f @2`[ key ] ( A , B )"
   (at level 24, format "f  @2`[ key ]  ( A ,  B )").
 Reserved Notation "f @` A" (at level 24).
 Reserved Notation "f @2` ( A , B )" (at level 24, format "f  @2`  ( A ,  B )").
 
 (* unary *)
 Reserved Notation "[ 'fset' E | x : T 'in' A ]" (at level 0, E, x at level 99).
@@ -168,9 +168,9 @@
 Reserved Notation "[ 'fset' x 'in' A | P & Q ]" (at level 0, x at level 99).
 
 (* binary *)
 Reserved Notation "[ 'fset' E | x : T 'in' A , y : T' 'in' B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99).
 Reserved Notation "[ 'fset' E | x 'in' A , y 'in' B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99).
 
 (* keyed parse only *)
@@ -183,11 +183,11 @@
   (at level 0, E, x at level 99).
 Reserved Notation "[ 'fset[' key ] E | x : A & P ]"
   (at level 0, E, x at level 99).
 Reserved Notation "[ 'fset[' key ] E | x : T 'in' A , y : T' 'in' B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99).
 Reserved Notation "[ 'fset[' key ] E | x 'in' A , y 'in' B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99).
 Reserved Notation "[ 'fset[' key ] E | x : A , y : B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99).
 Reserved Notation "[ 'fset[' key ] E | x : A , y 'in' B ]"
   (at level 0, E, x, y at level 99).
@@ -233,7 +233,7 @@
 Reserved Notation "[ 'f' 'set' x 'in' A | P & Q ]"
   (at level 0, x at level 99, format "[ 'f' 'set'  x  'in'  A  |  P  &  Q ]").
 (* binary printing only *)
 Reserved Notation "[ 'f' 'set' E | x 'in' A , y 'in' B ]"
   (at level 0, E, x at level 99, A at level 200, y at level 99,
    format "[ '[hv' 'f' 'set'  E '/ '  |  x  'in'  A , '/' y  'in'  B ] ']'").
 
@@ -339,7 +339,7 @@
   (at level 0, x at level 99, format "[ 'f' 'setval'  x  :  A  |  P  &  Q ]").
 
 Reserved Notation "{fmap T }" (at level 0, format "{fmap  T }").
 Reserved Notation "x .[ k <- v ]"
   (left associativity, format "x .[ k  <-  v ]").
 Reserved Notation "x .[~ k ]" (format "x .[~  k ]").
 Reserved Notation "x .[& k ]" (format "x .[&  k ]").
@@ -354,7 +354,7 @@
 Defined.
 Arguments PredType [T pT] toP.
 
 Local Notation predOfType T := (pred_of_simpl (@pred_of_argType T)).
 
 Definition oextract (T : Type) (o : option T) : o -> T :=
   if o is Some t return o -> T then fun=> t else False_rect T \o notF.
@@ -417,7 +417,7 @@
 
 #[global] Hint Resolve SortKeys.perm SortKeys.uniq SortKeys.E : core.
 
 Notation sort_keys      := SortKeys.f.
 Notation sort_keys_perm := SortKeys.perm.
 Notation sort_keys_uniq := SortKeys.uniq.
 Notation sort_keysE     := SortKeys.E.
@@ -593,7 +593,7 @@
 
 #[global] Hint Resolve keys_canonical sort_keys_uniq : core.
 
 HB.instance Definition _ K := [isSub for (@enum_fset K)].
 HB.instance Definition _ (K : choiceType) := [Choice of {fset K} by <:].
 
 Section FinPredStruct.
@@ -1902,6 +1902,9 @@
 by rewrite !(fsubset_trans _ subA).
 Qed.
 
+Lemma fsubU1set x A B : (x |` A `<=` B) = (x \in B) && (A `<=` B).
+Proof. by rewrite fsubUset fsub1set. Qed.
+
 Lemma fsubUsetP A B C : reflect (A `<=` C /\ B `<=` C) (A `|` B `<=` C).
 Proof. by rewrite fsubUset; exact: andP. Qed.