X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Flib%2Flambda%2Frc_hsat.ma;fp=matita%2Fmatita%2Flib%2Flambda%2Frc_hsat.ma;h=0000000000000000000000000000000000000000;hb=46e87acb755894f9234191d675eeb5db4f5b930b;hp=7426d812bb099d22e69b203787edf8d24f86482e;hpb=f8bc120b39bd74ade4e11d4d3ef4355f66c42495;p=helm.git diff --git a/matita/matita/lib/lambda/rc_hsat.ma b/matita/matita/lib/lambda/rc_hsat.ma deleted file mode 100644 index 7426d812b..000000000 --- a/matita/matita/lib/lambda/rc_hsat.ma +++ /dev/null @@ -1,63 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "lambda/rc_sat.ma". - -(* HIGHER ORDER REDUCIBILITY CANDIDATES ***************************************) - -(* An arity is a type of λ→ to be used as carrier for a h.o. r.c. *) - -(* The type of the higher order r.c.'s having a given carrier. - * a h.o. r.c is implemented as an inductively defined metalinguistic function - * [ a CIC function in the present case ]. - *) -let rec HRC P ≝ match P with - [ SORT ⇒ RC - | ABST Q P ⇒ HRC Q → HRC P - ]. - -(* The default h.o r.c. - * This is needed to complete the partial interpretation of types. - *) -let rec defHRC P ≝ match P return λP. HRC P with - [ SORT ⇒ snRC - | ABST Q P ⇒ λ_. defHRC P - ]. - -(* extensional equality *******************************************************) - -(* This is the extensional equalty of functions - * modulo the extensional equality on the domain. - * The functions may not respect extensional equality so reflexivity fails. - *) -let rec hrceq P ≝ match P return λP. HRC P → HRC P → Prop with - [ SORT ⇒ λC1,C2. C1 ≅ C2 - | ABST Q P ⇒ λC1,C2. ∀B1,B2. hrceq Q B1 B2 → hrceq P (C1 B1) (C2 B2) - ]. - -interpretation - "extensional equality (h.o. reducibility candidate)" - 'Eq1 P C1 C2 = (hrceq P C1 C2). - -lemma symmetric_hrceq: ∀P. symmetric ? (hrceq P). -#P (elim P) -P /4/ -qed. - -lemma transitive_hrceq: ∀P. transitive ? (hrceq P). -#P (elim P) -P /5/ -qed. - -lemma reflexive_defHRC: ∀P. defHRC P ≅^P defHRC P. -#P (elim P) -P (normalize) /2/ -qed.