X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda-delta%2FBasic-2%2Freduction%2Ftpr_tpr.ma;h=d0ae3fa90b47403a3f1b8e22d17b0e96f0a36f49;hb=ffe34220d80cba65eccf2396fba7f692cc6448c8;hp=aec243d136babbac559208323ab8a506f4bfe767;hpb=fd991956035d0f1b663aab48325097e53ed9e00e;p=helm.git

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/tpr_tpr.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/tpr_tpr.ma
index aec243d13..d0ae3fa90 100644
--- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/tpr_tpr.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/tpr_tpr.ma
@@ -26,48 +26,6 @@ lemma tpr_conf_sort_sort: ∀k. ∃∃X. ⋆k ⇒ X & ⋆k ⇒ X.
 lemma tpr_conf_lref_lref: ∀i. ∃∃X. #i ⇒ X & #i ⇒ X.
 /2/ qed.
 
-lemma tpr_conf_bind_bind:
-   ∀I,V0,V1,T0,T1,V2,T2. (
-      ∀X0:term. #X0 < #V0 + #T0 + 1 →
-      ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
-      ∃∃X. X1 ⇒ X & X2 ⇒ X
-   ) →
-   V0 ⇒ V1 → V0 ⇒ V2 → T0 ⇒ T1 → T0 ⇒ T2 →
-   ∃∃X. 𝕓{I} V1. T1 ⇒ X & 𝕓{I} V2. T2 ⇒ X.
-#I #V0 #V1 #T0 #T1 #V2 #T2 #IH #HV01 #HV02 #HT01 #HT02
-elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
-elim (IH … HT01 … HT02) -HT01 HT02 IH /3 width=5/
-qed.
-
-lemma tpr_conf_bind_delta:
-   ∀V0,V1,T0,T1,V2,T2,T. (
-      ∀X0:term. #X0 < #V0 + #T0 + 1 →
-      ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
-      ∃∃X. X1 ⇒ X & X2 ⇒ X
-   ) →
-   V0 ⇒ V1 → V0 ⇒ V2 →
-   T0 ⇒ T1 → T0 ⇒ T2 → ⋆. 𝕓{Abbr} V2 ⊢ T2 [O,1] ≫ T →
-   ∃∃X. 𝕓{Abbr} V1. T1 ⇒ X & 𝕓{Abbr} V2. T ⇒ X.
-#V0 #V1 #T0 #T1 #V2 #T2 #T #IH #HV01 #HV02 #HT01 #HT02 #HT2
-elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
-elim (IH … HT01 … HT02) -HT01 HT02 IH // -V0 T0 #T0 #HT10 #HT20
-elim (tpr_tps_bind … HV2 HT20 … HT2) -HT20 HT2 /3 width=5/
-qed.
-
-lemma tpr_conf_bind_zeta:
-   ∀X2,V0,V1,T0,T1,T. (
-      ∀X0:term. #X0 < #V0 + #T0 +1 →
-      ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
-      ∃∃X. X1 ⇒ X & X2 ⇒ X
-   ) →
-   V0 ⇒ V1 → T0 ⇒ T1 → T ⇒ X2 → ↑[O, 1] T ≡ T0 →
-   ∃∃X. 𝕓{Abbr} V1. T1 ⇒ X & X2 ⇒ X.
-#X2 #V0 #V1 #T0 #T1 #T #IH #HV01 #HT01 #HTX2 #HT0
-elim (tpr_inv_lift … HT01 … HT0) -HT01 #U #HUT1 #HTU
-lapply (tw_lift … HT0) -HT0 #HT0
-elim (IH … HTX2 … HTU) -HTX2 HTU IH /3/
-qed.
-
 lemma tpr_conf_flat_flat:
    ∀I,V0,V1,T0,T1,V2,T2. (
       ∀X0:term. #X0 < #V0 + #T0 + 1 →
@@ -110,13 +68,8 @@ elim (IH … HV01 … HV02) -HV01 HV02 // #VV #HVV1 #HVV2
 elim (lift_total VV 0 1) #VVV #HVV
 lapply (tpr_lift … HVV2 … HV2 … HVV) #HVVV
 elim (tpr_inv_abbr1 … H) -H *
-(* case 1: bind *)
-[ -HV2 HVV2 #WW #UU #HWW0 #HUU0 #H destruct -T1;
-  elim (IH … HW02 … HWW0) -HW02 HWW0 // #W #HW2 #HWW
-  elim (IH … HU02 … HUU0) -HU02 HUU0 IH // #U #HU2 #HUU
-  @ex2_1_intro [2: @tpr_theta |1:skip |3: @tpr_bind ] /2 width=7/ (**) (* /4 width=7/ is too slow *)
-(* case 2: delta *)
-| -HV2 HVV2 #WW2 #UU2 #UU #HWW2 #HUU02 #HUU2 #H destruct -T1;
+(* case 1: delta *)
+[ -HV2 HVV2 #WW2 #UU2 #UU #HWW2 #HUU02 #HUU2 #H destruct -T1;
   elim (IH … HW02 … HWW2) -HW02 HWW2 // #W #HW02 #HWW2
   elim (IH … HU02 … HUU02) -HU02 HUU02 IH // #U #HU2 #HUUU2
   elim (tpr_tps_bind … HWW2 HUUU2 … HUU2) -HUU2 HUUU2 #UUU #HUUU2 #HUUU1
@@ -164,16 +117,16 @@ elim (IH … HT01 … HT02) -HT01 HT02 IH /3 width=5/
 qed.
 
 lemma tpr_conf_delta_delta:
-   ∀V0,V1,T0,T1,TT1,V2,T2,TT2. (
+   ∀I1,V0,V1,T0,T1,TT1,V2,T2,TT2. (
       ∀X0:term. #X0 < #V0 +#T0 + 1→
       ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
       ∃∃X. X1 ⇒ X & X2 ⇒ X
    ) →
    V0 ⇒ V1 → V0 ⇒ V2 → T0 ⇒ T1 → T0 ⇒ T2 →
-   ⋆. 𝕓{Abbr} V1 ⊢ T1 [O, 1] ≫ TT1 →
-   ⋆. 𝕓{Abbr} V2 ⊢ T2 [O, 1] ≫ TT2 →
-   ∃∃X. 𝕓{Abbr} V1. TT1 ⇒ X & 𝕓{Abbr} V2. TT2 ⇒ X.
-#V0 #V1 #T0 #T1 #TT1 #V2 #T2 #TT2 #IH #HV01 #HV02 #HT01 #HT02 #HTT1 #HTT2
+   ⋆. 𝕓{I1} V1 ⊢ T1 [O, 1] ≫ TT1 →
+   ⋆. 𝕓{I1} V2 ⊢ T2 [O, 1] ≫ TT2 →
+   ∃∃X. 𝕓{I1} V1. TT1 ⇒ X & 𝕓{I1} V2. TT2 ⇒ X.
+#I1 #V0 #V1 #T0 #T1 #TT1 #V2 #T2 #TT2 #IH #HV01 #HV02 #HT01 #HT02 #HTT1 #HTT2
 elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
 elim (IH … HT01 … HT02) -HT01 HT02 IH // #T #HT1 #HT2
 elim (tpr_tps_bind … HV1 HT1 … HTT1) -HT1 HTT1 #U1 #TTU1 #HTU1
@@ -262,85 +215,67 @@ lemma tpr_conf_aux:
   lapply (tpr_inv_lref1 … H1) -H1
 (* case 2: lref, lref *)
   #H1 destruct -X2 //
-| #I #V0 #V1 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
-  elim (tpr_inv_bind1 … H1) -H1 *
-(* case 3: bind, bind *)
-  [ #V2 #T2 #HV02 #HT02 #H destruct -X2
-    /3 width=7 by tpr_conf_bind_bind/ (**) (* /3 width=7/ is too slow *)
-(* case 4: bind, delta *)
-  | #V2 #T2 #T #HV02 #HT02 #HT2 #H1 #H2 destruct -X2 I
-    /3 width=9 by tpr_conf_bind_delta/ (**) (* /3 width=9/ is too slow *)
-(* case 5: bind, zeta *)
-  | #T #HT0 #HTX2 #H destruct -I
-    /3 width=8 by tpr_conf_bind_zeta/ (**) (* /3 width=8/ is too slow *)
-  ]
 | #I #V0 #V1 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
   elim (tpr_inv_flat1 … H1) -H1 *
-(* case 6: flat, flat *)
+(* case 3: flat, flat *)
   [ #V2 #T2 #HV02 #HT02 #H destruct -X2
     /3 width=7 by tpr_conf_flat_flat/ (**) (* /3 width=7/ is too slow *)
-(* case 7: flat, beta *)
+(* case 4: flat, beta *)
   | #V2 #W #U0 #T2 #HV02 #HT02 #H1 #H2 #H3 destruct -T0 X2 I
     /3 width=8 by tpr_conf_flat_beta/ (**) (* /3 width=8/ is too slow *)
-(* case 8: flat, theta *)
+(* case 5: flat, theta *)
   | #V2 #V #W0 #W2 #U0 #U2 #HV02 #HW02 #HT02 #HV2 #H1 #H2 #H3 destruct -T0 X2 I
     /3 width=11 by tpr_conf_flat_theta/ (**) (* /3 width=11/ is too slow *)
-(* case 9: flat, tau *)
+(* case 6: flat, tau *)
   | #HT02 #H destruct -I
     /3 width=6 by tpr_conf_flat_cast/ (**) (* /3 width=6/ is too slow *)
   ]
 | #V0 #V1 #W0 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
   elim (tpr_inv_appl1 … H1) -H1 *
-(* case 10: beta, flat (repeated) *)
+(* case 7: beta, flat (repeated) *)
   [ #V2 #T2 #HV02 #HT02 #H destruct -X2
     @ex2_1_comm /3 width=8 by tpr_conf_flat_beta/
-(* case 11: beta, beta *)
+(* case 8: beta, beta *)
   | #V2 #WW0 #TT0 #T2 #HV02 #HT02 #H1 #H2 destruct -W0 T0 X2
     /3 width=8 by tpr_conf_beta_beta/ (**) (* /3 width=8/ is too slow *)
-(* case 12, beta, theta (excluded) *)
+(* case 9, beta, theta (excluded) *)
   | #V2 #VV2 #WW0 #W2 #TT0 #T2 #_ #_ #_ #_ #H destruct
   ]
-| #V0 #V1 #T0 #T1 #TT1 #HV01 #HT01 #HTT1 #H1 #H2 destruct -Y0;
-  elim (tpr_inv_abbr1 … H1) -H1 *
-(* case 13: delta, bind (repeated) *)
-  [ #V2 #T2 #HV02 #T02 #H destruct -X2
-    @ex2_1_comm /3 width=9 by tpr_conf_bind_delta/
-(* case 14: delta, delta *)
-  | #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
+| #I1 #V0 #V1 #T0 #T1 #TT1 #HV01 #HT01 #HTT1 #H1 #H2 destruct -Y0;
+  elim (tpr_inv_bind1 … H1) -H1 *
+(* case 10: delta, delta *)
+  [ #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
     /3 width=11 by tpr_conf_delta_delta/ (**) (* /3 width=11/ is too slow *)
-(* case 15: delta, zata *)
-  | #T2 #HT20 #HTX2
+(* case 11: delta, zata *)
+  | #T2 #HT20 #HTX2 #H destruct -I1;
     /3 width=10 by tpr_conf_delta_zeta/ (**) (* /3 width=10/ is too slow *)
   ]
 | #VV1 #V0 #V1 #W0 #W1 #T0 #T1 #HV01 #HVV1 #HW01 #HT01 #H1 #H2 destruct -Y0;
   elim (tpr_inv_appl1 … H1) -H1 *
-(* case 16: theta, flat (repeated) *)
+(* case 12: theta, flat (repeated) *)
   [ #V2 #T2 #HV02 #HT02 #H destruct -X2
     @ex2_1_comm /3 width=11 by tpr_conf_flat_theta/
-(* case 17: theta, beta (repeated) *)
+(* case 13: theta, beta (repeated) *)
   | #V2 #WW0 #TT0 #T2 #_ #_ #H destruct
-(* case 18: theta, theta *)
+(* case 14: theta, theta *)
   | #V2 #VV2 #WW0 #W2 #TT0 #T2 #V02 #HW02 #HT02 #HVV2 #H1 #H2 destruct -W0 T0 X2
-    /3 width=14 by tpr_conf_theta_theta/  (**) (* /3 width=14/ is too slow *)
+    /3 width=14 by tpr_conf_theta_theta/ (**) (* /3 width=14/ is too slow *)
   ]
 | #V0 #TT0 #T0 #T1 #HTT0 #HT01 #H1 #H2 destruct -Y0;
   elim (tpr_inv_abbr1 … H1) -H1 *
-(* case 19: zeta, bind (repeated) *)
-  [ #V2 #T2 #HV02 #T02 #H destruct -X2
-    @ex2_1_comm /3 width=8 by tpr_conf_bind_zeta/
-(* case 20: zeta, delta (repeated) *)
-  | #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
+(* case 15: zeta, delta (repeated) *)
+  [ #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
     @ex2_1_comm /3 width=10 by tpr_conf_delta_zeta/
-(* case 21: zeta, zeta *)
+(* case 16: zeta, zeta *)
   | #T2 #HTT20 #HTX2
     /3 width=9 by tpr_conf_zeta_zeta/ (**) (* /3 width=9/ is too slow *)
   ] 
 | #V0 #T0 #T1 #HT01 #H1 #H2 destruct -Y0;
   elim (tpr_inv_cast1 … H1) -H1
-(* case 22: tau, flat (repeated) *)
+(* case 17: tau, flat (repeated) *)
   [ * #V2 #T2 #HV02 #HT02 #H destruct -X2
     @ex2_1_comm /3 width=6 by tpr_conf_flat_cast/
-(* case 23: tau, tau *)
+(* case 18: tau, tau *)
   | #HT02
     /2 by tpr_conf_tau_tau/
   ]