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Commit 268f865e authored by François Clément's avatar François Clément
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Mv.

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......@@ -406,6 +406,14 @@ intros PA B [BA HBA]; unfold Lift_full;
rewrite <- (compose_eq (trace _)), trace_lift; easy.
Qed.
Lemma Trace_equiv :
forall (P : set_system U) B, Trace A P B <-> exists C, P C /\ B = trace A C.
Proof.
intros B; split.
intros [C HC]; exists C; easy.
intros [C [HC HB]]; rewrite HB; easy.
Qed.
Lemma Lift_Trace : compose (Lift A) (Trace A) = interp_map_any_r A.
Proof.
unfold Lift, Trace; setp_any_unfold.
......@@ -447,14 +455,6 @@ apply Lift_Lift_full.
rewrite <- compose_eq, Trace_Lift; easy.
Qed.
Lemma Trace_equiv :
forall (P : set_system U) B, Trace A P B <-> exists C, P C /\ B = trace A C.
Proof.
intros B; split.
intros [C HC]; exists C; easy.
intros [C [HC HB]]; rewrite HB; easy.
Qed.
Lemma Lift_Incl_Incl_Trace :
forall (PA : subset_system A) (P : set_system U),
Incl (Lift A PA) P -> Incl PA (Trace A P).
......
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