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(** Author: Cristina Cornes From : Constructing Recursion Operators in Type Theory L. Paulson  JSC (1986) 2, 325-355 *)
Section Wf_Disjoint_Union.
Variables A B : Type.
Variable leA : A -> A -> Prop.
Variable leB : B -> B -> Prop.
Notation Le_AsB := (le_AsB A B leA leB).

(* Specifications: *)
Lemma acc_A_sum : forall x:A, Acc leA x -> Acc Le_AsB (inl B x).
Lemma acc_B_sum :
well_founded leA -> forall x:B, Acc leB x -> Acc Le_AsB (inr A x).
Lemma wf_disjoint_sum :
well_founded leA -> well_founded leB -> well_founded Le_AsB.