Goal:
    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
idtac

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
sets

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
VSetDecide.fsetdec

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++;
            VSetDecide.MSetDecideAuxiliary.Logic_eq_to_E_eq; pull not using
            MSet_decidability; unfold not in *;
            match goal with
            | H:VSet.In ?x ?r -> False
              |- VSet.In ?x ?s -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:VSet.In ?x ?r -> False
              |- ?x = ?y -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:VSet.In ?x ?r -> False
              |- ?y = ?x -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:?P -> False
              |- ?Q -> False =>
                  tryif prop (VSetDecide.MSetDecideAuxiliary.MSet_elt_Prop P)
                   holds by auto  100 with MSet_Prop then
                   (contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body)
                    else VSetDecide.MSetDecideAuxiliary.fsetdec_body 
            | |- _ => VSetDecide.MSetDecideAuxiliary.fsetdec_body
            end

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++;
            VSetDecide.MSetDecideAuxiliary.Logic_eq_to_E_eq; pull not using
            MSet_decidability; unfold not in *

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++;
            VSetDecide.MSetDecideAuxiliary.Logic_eq_to_E_eq; pull not using
            MSet_decidability

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++;
            VSetDecide.MSetDecideAuxiliary.Logic_eq_to_E_eq

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not; intros

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *; fold any not

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   (VSet.In y (VSet.add x s) <-> x = y \/ VSet.In y (VSet.remove x s))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
unfold iff in *

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   ((VSet.In y (VSet.add x s) -> x = y \/ VSet.In y (VSet.remove x s)) /\
    (x = y \/ VSet.In y (VSet.remove x s) -> VSet.In y (VSet.add x s)))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
fold any not

Goals:
    x : V.t  s : VSet.t  y : VSet.elt
  ============================
   ((VSet.In y (VSet.add x s) -> x = y \/ VSet.In y (VSet.remove x s)) /\
    (x = y \/ VSet.In y (VSet.remove x s) -> VSet.In y (VSet.add x s)))

    x : V.t  s : VSet.t
  ============================
   (~ VSet.In x (VSet.remove x s))


DEBUG:Going to execute:
repeat
            match goal with
            | H:context [ ?P -> False ] |- _ => fold (~ P) in H
            | |- context [ ?P -> False ] => fold (~ P)
            end