(* *)
(**************************************************************************)
-include "ground_2/xoa/ex_2_4.ma".
include "basic_2/notation/relations/pconveta_5.ma".
include "basic_2/rt_computation/cpms.ma".
| cpce_ldef: ∀G,K,V. cpce h G (K.ⓓV) (#0) (#0)
| cpce_ldec: ∀n,G,K,V,s. ⦃G,K⦄ ⊢ V ➡*[n,h] ⋆s →
cpce h G (K.ⓛV) (#0) (#0)
-| cpce_eta : ∀n,p,G,K,V,W,T. ⦃G,K⦄ ⊢ V ➡*[n,h] ⓛ{p}W.T →
- cpce h G (K.ⓛV) (#0) (+ⓛW.ⓐ#0.#1)
+| cpce_eta : ∀n,p,G,K,V,W1,W2,T. ⦃G,K⦄ ⊢ V ➡*[n,h] ⓛ{p}W1.T →
+ cpce h G K W1 W2 → cpce h G (K.ⓛV) (#0) (+ⓛW2.ⓐ#0.#1)
| cpce_lref: ∀I,G,K,T,U,i. cpce h G K (#i) T →
⬆*[1] T ≘ U → cpce h G (K.ⓘ{I}) (#↑i) U
| cpce_bind: ∀p,I,G,K,V1,V2,T1,T2.
.
interpretation
- "context-sensitive parallel eta-conversion (term)"
- 'PConvEta h G L T1 T2 = (cpce h G L T1 T2).
+ "context-sensitive parallel eta-conversion (term)"
+ 'PConvEta h G L T1 T2 = (cpce h G L T1 T2).
(* Basic inversion lemmas ***************************************************)
[ #G #L #s #_ //
| #G #K #V #_ //
| #n #G #K #V #s #_ #_ //
-| #n #p #G #K #V #W #T #_ #H destruct
+| #n #p #G #K #V #W1 #W2 #T #_ #_ #H destruct
| #I #G #K #T #U #i #_ #_ #H destruct
| #p #I #G #K #V1 #V2 #T1 #T2 #_ #_ #H destruct
| #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H destruct
[ #G #L #s #_ #_ //
| #G #K #V #_ #_ //
| #n #G #K #V #s #_ #_ #_ //
-| #n #p #G #K #V #W #T #_ #_ #H destruct
+| #n #p #G #K #V #W1 #W2 #T #_ #_ #_ #H destruct
| #I #G #K #T #U #i #_ #_ #H #_ destruct
| #p #I #G #K #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
| #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
lemma cpce_inv_ldec_sn (h) (G) (K) (X2):
∀V. ⦃G,K.ⓛV⦄ ⊢ #0 ⬌η[h] X2 →
∨∨ ∃∃n,s. ⦃G,K⦄ ⊢ V ➡*[n,h] ⋆s & #0 = X2
- | ∃∃n,p,W,T. ⦃G,K⦄ ⊢ V ➡*[n,h] ⓛ{p}W.T & +ⓛW.ⓐ#0.#1 = X2.
+ | ∃∃n,p,W1,W2,T. ⦃G,K⦄ ⊢ V ➡*[n,h] ⓛ{p}W1.T & ⦃G,K⦄ ⊢ W1 ⬌η[h] W2 & +ⓛW2.ⓐ#0.#1 = X2.
#h #G #Y #X2 #X
@(insert_eq_0 … (Y.ⓛX)) #Y1
@(insert_eq_0 … (#0)) #X1
[ #G #L #s #H #_ destruct
| #G #K #V #_ #H destruct
| #n #G #K #V #s #HV #_ #H destruct /3 width=3 by ex2_2_intro, or_introl/
-| #n #p #G #K #V #W #T #HV #_ #H destruct /3 width=6 by or_intror, ex2_4_intro/
+| #n #p #G #K #V #W1 #W2 #T #HV #HW #_ #H destruct /3 width=8 by ex3_5_intro, or_intror/
| #I #G #K #T #U #i #_ #_ #H #_ destruct
| #p #I #G #K #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
| #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
[ #G #L #s #H #_ destruct
| #G #K #V #H #_ destruct
| #n #G #K #V #s #_ #H #_ destruct
-| #n #p #G #K #V #W #T #_ #H #_ destruct
+| #n #p #G #K #V #W1 #W2 #T #_ #_ #H #_ destruct
| #I #G #K #T #U #i #Hi #HTU #H1 #H2 destruct /2 width=3 by ex2_intro/
| #p #I #G #K #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
| #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H #_ destruct
[ #G #L #s #H destruct
| #G #K #V #H destruct
| #n #G #K #V #s #_ #H destruct
-| #n #p #G #K #V #W #T #_ #H destruct
+| #n #p #G #K #V #W1 #W2 #T #_ #_ #H destruct
| #I #G #K #T #U #i #_ #_ #H destruct
| #p #I #G #K #V1 #V2 #T1 #T2 #HV #HT #H destruct /2 width=5 by ex3_2_intro/
| #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H destruct
[ #G #L #s #H destruct
| #G #K #V #H destruct
| #n #G #K #V #s #_ #H destruct
-| #n #p #G #K #V #W #T #_ #H destruct
+| #n #p #G #K #V #W1 #W2 #T #_ #_ #H destruct
| #I #G #K #T #U #i #_ #_ #H destruct
| #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #H destruct
| #I #G #K #V1 #V2 #T1 #T2 #HV #HT #H destruct /2 width=5 by ex3_2_intro/