### Use simple apply in f_equiv and solve_proper.

```As suggested by Pierre-Marie Pédrot in the Coq-club thread:

[Coq-Club] Very slow failing apply

To work arround some performance issues in Iris.```
parent 7891aa0b
 ... ... @@ -286,39 +286,39 @@ Ltac f_equiv := | H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) => destruct H (* First assume that the arguments need the same relation as the result *) | |- ?R (?f _) _ => apply (_ : Proper (R ==> R) f) | |- ?R (?f _ _) _ => apply (_ : Proper (R ==> R ==> R) f) | |- ?R (?f _ _ _) _ => apply (_ : Proper (R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _ _) _ => apply (_ : Proper (R ==> R ==> R ==> R ==> R) f) | |- ?R (?f _) _ => simple apply (_ : Proper (R ==> R) f) | |- ?R (?f _ _) _ => simple apply (_ : Proper (R ==> R ==> R) f) | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f) (* For the case in which R is polymorphic, or an operational type class, like equiv. *) | |- (?R _) (?f _) _ => apply (_ : Proper (R _ ==> _) f) | |- (?R _ _) (?f _) _ => apply (_ : Proper (R _ _ ==> _) f) | |- (?R _ _ _) (?f _) _ => apply (_ : Proper (R _ _ _ ==> _) f) | |- (?R _) (?f _ _) _ => apply (_ : Proper (R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _) (?f _ _ _) _ => apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f) | |- (?R _) (?f _ _ _ _) _ => apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _ _) _ => apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _ _) _ => apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> R _ _ _ ==> _) f) | |- (?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 _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _) (?f _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f) | |- (?R _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f) | |- (?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. *) (* 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 _) _ => apply (_ : Proper (_ ==> R) f) | |- ?R (?f _ _) _ => apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f _ _ _) _ => apply (_ : Proper (_ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _ _) _ => 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) | |- ?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. *) | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => apply H | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => simple apply H end; try reflexivity. try simple apply reflexivity. (* The tactic [solve_proper_unfold] unfolds the first head symbol, so that we proceed by repeatedly using [f_equiv]. *) ... ...
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