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Axiom hp : Set.
Axiom cont : nat -> hp -> Prop.
Axiom sconj : (hp -> Prop) -> (hp -> Prop) -> hp -> Prop.
Axiom sconjImpl : forall h A B,
(sconj A B) h -> forall (A' B': hp -> Prop),
(forall h', A h' -> A' h') ->
(forall h', B h' -> B' h') ->
(sconj A' B') h.
Definition cont' (h:hp) := exists y, cont y h.
Lemma foo : forall h x y A,
(sconj (cont x) (sconj (cont y) A)) h ->
(sconj cont' (sconj cont' A)) h.
Proof.
intros h x y A H.
eapply sconjImpl.
2:intros h' Hp'; econstructor; apply Hp'.
2:intros h' Hp'; eapply sconjImpl.
3:intros h'' Hp''; econstructor; apply Hp''.
3:intros h'' Hp''; apply Hp''.
2:apply Hp'.
clear H.
Admitted.
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