val closure_reflexive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (reflexive (_closure0 r))
let closure_reflexive #a r =
  assert (forall x. _closure0 r x x) by
    (let x = forall_intro () in
     mapply (`FStar.Squash.return_squash);
     mapply (`Refl))
val closure_reflexive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (reflexive (_closure0 r))
let closure_reflexive #a r =
FStar.Tactics.Effect.assert_by_tactic (forall x. _closure0 r x x)
  (fun _ ->
      ();
      (let x = forall_intro () in
        mapply (`FStar.Squash.return_squash);
        mapply (`Refl)))
FStar.ReflexiveTransitiveClosure.fst.checked
prims.fst.checked FStar.Tactics.V2.fst.checked FStar.Tactics.Effect.fsti.checked FStar.Squash.fsti.checked FStar.Pervasives.fsti.checked
FStar.ReflexiveTransitiveClosure.fst
FStar.ReflexiveTransitiveClosure.binrel FStar.Tactics.Effect.assert_by_tactic Prims.l_Forall FStar.ReflexiveTransitiveClosure._closure0 Prims.unit FStar.Tactics.MApply.mapply FStar.Reflection.Types.term FStar.Tactics.MApply.termable_term FStar.Tactics.NamedView.binding FStar.Tactics.V2.Logic.forall_intro
(*
   Copyright 2008-2019 Microsoft Research

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.
*)
module FStar.ReflexiveTransitiveClosure

open FStar.Tactics.V2
#set-options "--max_ifuel 1 --max_fuel 0"

noeq
type _closure (#a:Type u#a) (r:binrel u#a u#r a) : a -> a -> Type u#(max a r) =
| Refl: x:a -> _closure r x x
| Step: x:a -> y:a -> squash (r x y) ->_closure r x y
| Closure: x:a -> y:a -> z:a -> _closure r x y -> _closure r y z -> _closure r x z

let _closure0 (#a:Type) (r:binrel a) (x y: a) : prop =
  squash (_closure r x y)

let get_squash (#a:Type) (r:binrel a) (x:a) (y:a{_closure0 r x y})
  : Tot (squash (_closure r x y))
  = assert_norm (_closure0 r x y ==> squash (_closure r x y))

val closure_reflexive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (reflexive (_closure0 r))
val closure_reflexive: #a:Type u#a -> r:binrel u#a u#r a -> Lemma (reflexive (_closure0 r))
r: FStar.ReflexiveTransitiveClosure.binrel a
  -> FStar.Pervasives.Lemma
    (ensures
      FStar.ReflexiveTransitiveClosure.reflexive (FStar.ReflexiveTransitiveClosure._closure0 r))