Ltac rel_curry_set_le_transport keyword :=
lazymatch goal with
| |- @Transport ?A ?B ?R ?a ?b ?PA ?PB =>
lazymatch PA with
| context [keyword] =>
let Xv := fresh "X" in evar (Xv: Type);
let X := eval red in Xv in clear Xv;
let Yv := fresh "Y" in evar (Yv: Type);
let Y := eval red in Yv in clear Yv;
unify B (X -> Y -> Prop);
eapply rel_curry_set_le_transport
end
end.

(* Specifications: *)
Lemma rel_curry2_set_le_transport {A1 A2 A3 B1 B2 B3} R sA sB (a1: A1) (a2: A2) (a3: A3):
Transport (% % set_le R) sA sB
(sA a1 a2 a3)
(exists (b1: B1) (b2: B2) (b3: B3), sB b1 b2 b3 /\ R (a1, a2, a3) (b1, b2, b3)).