Commit 461bc9c9 authored by Ralf Jung's avatar Ralf Jung

f_equiv: comments

parent e1fff8e2
......@@ -304,18 +304,18 @@ Ltac f_equiv :=
| |- (?R _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f)
| |- (?R _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
| |- (?R _ _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> R _ _ _ ==> _) f)
(* Next, try to infer the relation. Unfortunately, there is an instance
of Proper for (eq ==> _), which will always be matched. *)
(* Next, try to infer the relation. Unfortunately, very often, it will turn
the goal into a Leibniz equality so we get stuck. *)
(* TODO: Can we exclude that instance? *)
(* TODO: If some of the arguments are the same, we could also
query for "pointwise_relation"'s. But that leads to a combinatorial
explosion about which arguments are and which are not the same. *)
| |- ?R (?f _) _ => simple apply (_ : Proper (_ ==> R) f)
| |- ?R (?f _ _) _ => simple apply (_ : Proper (_ ==> _ ==> R) f)
| |- ?R (?f _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f)
| |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f)
(* In case the function symbol differs, but the arguments are the same,
maybe we have a pointwise_relation in our context. *)
(* In case the function symbol differs, but the arguments are the same,
maybe we have a pointwise_relation in our context. *)
(* TODO: If only some of the arguments are the same, we could also
query for "pointwise_relation"'s. But that leads to a combinatorial
explosion about which arguments are and which are not the same. *)
| H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => simple apply H
end;
try simple apply reflexivity.
......
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