diff options
Diffstat (limited to 'theories/Classes/SetoidTactics.v')
| -rw-r--r-- | theories/Classes/SetoidTactics.v | 28 |
1 files changed, 28 insertions, 0 deletions
diff --git a/theories/Classes/SetoidTactics.v b/theories/Classes/SetoidTactics.v index 4832f1d72..7be514169 100644 --- a/theories/Classes/SetoidTactics.v +++ b/theories/Classes/SetoidTactics.v @@ -35,3 +35,31 @@ Ltac setoideq := [ |- @eq ?A ?X ?Y ] => apply (setoideq_eq (a:=A) X Y) end. +Ltac setoid_tactic := + match goal with + | [ H : ?eq ?x ?y |- ?eq ?y ?x ] => sym ; apply H + | [ |- ?eq ?x ?x ] => refl + | [ H : ?eq ?x ?y, H' : ?eq ?y ?z |- ?eq' ?x ?z ] => trans y ; [ apply H | apply H' ] + | [ H : ?eq ?x ?y, H' : ?eq ?z ?y |- ?eq' ?x ?z ] => trans y ; [ apply H | sym ; apply H' ] + | [ H : ?eq ?y ?x, H' : ?eq ?z ?y |- ?eq' ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ] + | [ H : ?eq ?y ?x, H' : ?eq ?y ?z |- ?eq' ?x ?z ] => trans y ; [ sym ; apply H | apply H' ] + + | [ H : ?eq ?x ?y |- @equiv _ _ _ ?y ?x ] => sym ; apply H + | [ |- @equiv _ _ _ ?x ?x ] => refl + | [ H : ?eq ?x ?y, H' : ?eq ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | apply H' ] + | [ H : ?eq ?x ?y, H' : ?eq ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | sym ; apply H' ] + | [ H : ?eq ?y ?x, H' : ?eq ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ] + | [ H : ?eq ?y ?x, H' : ?eq ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | apply H' ] + + | [ H : @equiv ?A ?R ?s ?x ?y |- @equiv _ _ _ ?y ?x ] => sym ; apply H + | [ |- @equiv _ _ _ ?x ?x ] => refl + | [ H : @equiv ?A ?R ?s ?x ?y, H' : @equiv ?A ?R ?s ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | apply H' ] + | [ H : @equiv ?A ?R ?s ?x ?y, H' : @equiv ?A ?R ?s ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | sym ; apply H' ] + | [ H : @equiv ?A ?R ?s ?y ?x, H' : @equiv ?A ?R ?s ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ] + | [ H : @equiv ?A ?R ?s ?y ?x, H' : @equiv ?A ?R ?s ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | apply H' ] + + | [ H : not (@equiv ?A ?R ?s ?X ?X) |- _ ] => elim H ; refl + | [ H : not (@equiv ?A ?R ?s ?X ?Y), H' : @equiv ?A ?R ?s ?Y ?X |- _ ] => elim H ; sym ; apply H + | [ H : not (@equiv ?A ?R ?s ?X ?Y), H' : ?R ?Y ?X |- _ ] => elim H ; sym ; apply H + | [ H : not (@equiv ?A ?R ?s ?X ?Y) |- False ] => elim H ; clear H ; setoid_tac + end. |