bail out early for trivial hyps

theories/lithium/base.v

@@ -63,6 +63,20 @@ Ltac get_head e :=
   | _    => constr:(e)
   end.
 
+(** A version of done that does not exploit False and contradictions. *)
+Ltac done_no_false :=
+  solve
+  [ repeat first
+    [ fast_done
+    | solve [trivial]
+    (* All the tactics below will introduce themselves anyway, or make no sense
+       for goals of product type. So this is a good place for us to do it. *)
+    | progress intros
+    | solve [symmetry; trivial]
+    | solve [apply not_symmetry; trivial]
+    | split ]
+  ].
+
 (* Checks that a term is closed using a trick by Jason Gross. *)
 Ltac check_closed t :=
   assert_succeeds (

theories/lithium/interpreter.v

@@ -592,6 +592,9 @@ Ltac liImpl :=
   | |- ?P -> ?Q =>
     lazymatch type of P with
     | Prop => first [
+              (* first check if the hyp is trivial *)
+              assert_succeeds (assert (P) as _;[done_no_false|]); intros _
+            |
               progress normalize_goal_impl; simpl
             |
             (*