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Require Import Coq.Classes.RelationClasses.
Tactic Notation "etransitivity" open_constr(y) :=
intros;
let R := match goal with |- ?R ?x ?z => constr:(R) end in
let x := match goal with |- ?R ?x ?z => constr:(x) end in
let z := match goal with |- ?R ?x ?z => constr:(z) end in
let pre_proof_term_head := constr:(@transitivity _ R _) in
let proof_term_head := (eval cbn in pre_proof_term_head) in
refine (proof_term_head x y z _ _); [ change (R x y) | change (R y z) ].
(** We call [Coq.Init.Notations.etransitivity] for compatibility
because it's more powerful than [etransitivity _] in some cases,
e.g., when things need to be unfolded. *)
Tactic Notation "etransitivity" := Coq.Init.Notations.etransitivity.
Tactic Notation "etransitivity_rev" uconstr(y) := [ > etransitivity y; cycle 1.. ].
Tactic Notation "etransitivity_rev" := [ > etransitivity; cycle 1.. ].
Ltac transitivity_rev y := [ > transitivity y; cycle 1.. ].
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