Hint Resolve residuals_subst_rec.
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(* The Commutation Theorem *)
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(* Specifications: *)
Theorem commutation :
forall U1 U2 U3 V1 V2 V3 : redexes,
residuals U1 U2 U3 ->
residuals V1 V2 V3 ->
residuals (subst_r V1 U1) (subst_r V2 U2) (subst_r V3 U3).
Lemma residuals_comp : forall U V W : redexes, residuals U V W -> comp U V.
Lemma preservation1 :
forall U V UV : redexes,
residuals U V UV ->
forall (T : redexes) (UVT : union U V T), residuals T V UV.
Lemma preservation :
forall U V W UV : redexes,
union U V W -> residuals U V UV -> residuals W V UV.
Lemma mutual_residuals_comp :
forall (W U UW : redexes) (RU : residuals U W UW)
(V VW : redexes) (RV : residuals V W VW), comp UW VW.