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-rwxr-xr-xtheories/Relations/Operators_Properties.v12
-rwxr-xr-xtheories/Relations/Relations.v4
2 files changed, 8 insertions, 8 deletions
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v
index 5c3a46529..d7cb7a7eb 100755
--- a/theories/Relations/Operators_Properties.v
+++ b/theories/Relations/Operators_Properties.v
@@ -31,7 +31,7 @@ Apply Build_preorder.
Exact (rt_refl A R).
Exact (rt_trans A R).
-Save.
+Qed.
@@ -42,7 +42,7 @@ Red.
Induction 1; Auto with sets.
Intros.
Apply rt_trans with y0; Auto with sets.
-Save.
+Qed.
Lemma clos_refl_trans_ind_left: (A:Set)(R:A->A->Prop)(M:A)(P:A->Prop)
(P M)
@@ -61,7 +61,7 @@ Apply H0; Auto with sets.
Intros.
Apply H5 with P0; Auto with sets.
Apply rt_trans with y; Auto with sets.
-Save.
+Qed.
End Clos_Refl_Trans.
@@ -75,7 +75,7 @@ Red.
Induction 1; Auto with sets.
Intros.
Apply rst_trans with y0; Auto with sets.
-Save.
+Qed.
Lemma clos_rst_is_equiv: (equivalence A (clos_refl_sym_trans A R)).
Apply Build_equivalence.
@@ -84,7 +84,7 @@ Exact (rst_refl A R).
Exact (rst_trans A R).
Exact (rst_sym A R).
-Save.
+Qed.
Lemma clos_rst_idempotent:
(incl (clos_refl_sym_trans A (clos_refl_sym_trans A R))
@@ -93,7 +93,7 @@ Red.
Induction 1; Auto with sets.
Intros.
Apply rst_trans with y0; Auto with sets.
-Save.
+Qed.
End Clos_Refl_Sym_Trans.
diff --git a/theories/Relations/Relations.v b/theories/Relations/Relations.v
index 60cb9b4d7..86627c8b3 100755
--- a/theories/Relations/Relations.v
+++ b/theories/Relations/Relations.v
@@ -16,7 +16,7 @@ Lemma inverse_image_of_equivalence : (A,B:Set)(f:A->B)
(r:(relation B))(equivalence B r)->(equivalence A [x,y:A](r (f x) (f y))).
Intros; Split; Elim H; Red; Auto.
Intros; Apply equiv_trans with (f y); Assumption.
-Save.
+Qed.
Lemma inverse_image_of_eq : (A,B:Set)(f:A->B)
(equivalence A [x,y:A](f x)=(f y)).
@@ -25,4 +25,4 @@ Split; Red;
| (* transitivity *) Intros; Transitivity (f y); Assumption
| (* symmetry *) Intros; Symmetry; Assumption
].
-Save.
+Qed.