- support for atomic arities and candidates of reducibility started

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / ltpss_tpss.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
index 367093b0a181ff3755302a6b9ab2819f806f01b3..c75119b66af51e71a2ce56cf1f1299e9120ff520 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
@@ -24,28 +24,28 @@ lemma ltpss_tpss_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 →
                            d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2.
 #L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0 //
 #L #L0 #_ #HL0 #IHL #T2 #U2 #d2 #e2 #HTU2 #Hde1d2
-lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 HTU2 /2/
+lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 -HTU2 /2 width=1/
 qed.
 
 lemma ltpss_tps_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 →
                           ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
                           d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2.
 #L1 #L0 #d1 #e1 #HL10 #T2 #U2 #d2 #e2 #HTU2 #Hde1d2
-@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2/ (**) (* /3 width=6/ is too slow *)
+@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2 width=1/ (**) (* /3 width=6/ is too slow *)
 qed.
 
 lemma ltpss_tpss_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 →
                            ∀T2,U2. L1 ⊢ T2 [d, e] ≫* U2 → L0 ⊢ T2 [d, e] ≫* U2.
 #L0 #L1 #d #e #H @(ltpss_ind … H) -L1
-[ /2/
+[ /2 width=1/
 | #L #L1 #_ #HL1 #IHL #T2 #U2 #HTU2
-  lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 HTU2 /2/
+  lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 -HTU2 /2 width=1/
 ]
 qed.
 
 lemma ltpss_tps_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 →
                           ∀T2,U2. L1 ⊢ T2 [d, e] ≫ U2 → L0 ⊢ T2 [d, e] ≫* U2.
-/3/ qed.
+/3 width=3/ qed.
 
 lemma ltpss_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → 
                           L0 ⊢ T2 [d2, e2] ≫* U2 → L0 [d1, e1] ≫* L1 →
@@ -53,7 +53,7 @@ lemma ltpss_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 →
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #H @(ltpss_ind … H) -L1
 [ //
 | -HTU2 #L #L1 #_ #HL1 #IHL
-  lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 IHL //
+  lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 -IHL //
 ]
 qed.
 
@@ -61,45 +61,45 @@ lemma ltpss_tps_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 →
                          L0 ⊢ T2 [d2, e2] ≫ U2 → L0 [d1, e1] ≫* L1 →
                          L1 ⊢ T2 [d2, e2] ≫* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #HL01
-@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2/ (**) (* /3 width=6/ is too slow *)
+@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2 width=1/ (**) (* /3 width=6/ is too slow *)
 qed.
 
 lemma ltpss_tpss_conf_eq: ∀L0,L1,T2,U2,d,e.
                           L0 ⊢ T2 [d, e] ≫* U2 → L0 [d, e] ≫* L1 →
                           ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T.
 #L0 #L1 #T2 #U2 #d #e #HTU2 #H @(ltpss_ind … H) -L1
-[ /2/
+[ /2 width=3/
 | -HTU2 #L #L1 #_ #HL1 * #W2 #HTW2 #HUW2
   elim (ltps_tpss_conf … HL1 HTW2) -HTW2 #T #HT2 #HW2T
-  elim (ltps_tpss_conf … HL1 HUW2) -HL1 HUW2 #U #HU2 #HW2U
-  elim (tpss_conf_eq … HW2T … HW2U) -HW2T HW2U #V #HTV #HUV
-  lapply (tpss_trans_eq … HT2 … HTV) -T;
-  lapply (tpss_trans_eq … HU2 … HUV) -U /2/
+  elim (ltps_tpss_conf … HL1 HUW2) -HL1 -HUW2 #U #HU2 #HW2U
+  elim (tpss_conf_eq … HW2T … HW2U) -HW2T -HW2U #V #HTV #HUV
+  lapply (tpss_trans_eq … HT2 … HTV) -T
+  lapply (tpss_trans_eq … HU2 … HUV) -U /2 width=3/
 ]
 qed.
 
 lemma ltpss_tps_conf_eq: ∀L0,L1,T2,U2,d,e.
                          L0 ⊢ T2 [d, e] ≫ U2 → L0 [d, e] ≫* L1 →
                          ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T.
-/3/ qed.
+/3 width=3/ qed.
 
 lemma ltpss_tpss_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫* T2 →
                        ∀L2,ds,es. L1 [ds, es] ≫* L2 → 
                        ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T.
 #L1 #T1 #T2 #d #e #HT12 #L2 #ds #es #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=3/
 | #L #L2 #HL1 #HL2 * #T #HT1 #HT2
   elim (ltps_tpss_conf … HL2 HT1) -HT1 #T0 #HT10 #HT0
-  lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 HT0 #HT0
-  lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 HT0 #HT0
-  lapply (tpss_trans_eq … HT2 … HT0) -T /2/
+  lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 -HT0 #HT0
+  lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 -HT0 #HT0
+  lapply (tpss_trans_eq … HT2 … HT0) -T /2 width=3/
 ]
 qed.
 
 lemma ltpss_tps_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫ T2 →
                       ∀L2,ds,es. L1 [ds, es] ≫* L2 → 
                       ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T.
-/3/ qed.
+/3 width=1/ qed.
 
 (* Advanced properties ******************************************************)
 
@@ -107,10 +107,10 @@ lemma ltpss_tps2: ∀L1,L2,I,e.
                   L1 [0, e] ≫* L2 → ∀V1,V2. L2 ⊢ V1 [0, e] ≫ V2 →
                   L1. 𝕓{I} V1 [0, e + 1] ≫* L2. 𝕓{I} V2.
 #L1 #L2 #I #e #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=1/
 | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12
   elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2
-  lapply (IHL … HV1) -IHL HV1 #HL1
+  lapply (IHL … HV1) -IHL -HV1 #HL1
   @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
@@ -119,17 +119,17 @@ lemma ltpss_tps2_lt: ∀L1,L2,I,V1,V2,e.
                      L1 [0, e - 1] ≫* L2 → L2 ⊢ V1 [0, e - 1] ≫ V2 →
                      0 < e → L1. 𝕓{I} V1 [0, e] ≫* L2. 𝕓{I} V2.
 #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
->(plus_minus_m_m e 1) /2/
+>(plus_minus_m_m e 1) // /2 width=1/
 qed.
 
 lemma ltpss_tps1: ∀L1,L2,I,d,e. L1 [d, e] ≫* L2 →
                   ∀V1,V2. L2 ⊢ V1 [d, e] ≫ V2 →
                   L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
 #L1 #L2 #I #d #e #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=1/
 | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12
   elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2
-  lapply (IHL … HV1) -IHL HV1 #HL1
+  lapply (IHL … HV1) -IHL -HV1 #HL1
   @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
@@ -138,7 +138,7 @@ lemma ltpss_tps1_lt: ∀L1,L2,I,V1,V2,d,e.
                      L1 [d - 1, e] ≫* L2 → L2 ⊢ V1 [d - 1, e] ≫ V2 →
                      0 < d → L1. 𝕓{I} V1 [d, e] ≫* L2. 𝕓{I} V2.
 #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd
->(plus_minus_m_m d 1) /2/
+>(plus_minus_m_m d 1) // /2 width=1/
 qed.
 
 (* Advanced forward lemmas **************************************************)
@@ -148,12 +148,12 @@ lemma ltpss_fwd_tpss21: ∀e,K1,I,V1,L2. 0 < e → K1. 𝕓{I} V1 [0, e] ≫* L2
                                  L2 = K2. 𝕓{I} V2.
 #e #K1 #I #V1 #L2 #He #H @(ltpss_ind … H) -L2
 [ /2 width=5/
-| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L;
+| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct
   elim (ltps_inv_tps21 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H
   lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2
   lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/
 ]
-qed.
+qed-.
 
 lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. 𝕓{I} V1 [d, e] ≫* L2 →
                         ∃∃K2,V2. K1 [d - 1, e] ≫* K2 &
@@ -161,9 +161,9 @@ lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. 𝕓{I} V1 [d, e] ≫*
                                  L2 = K2. 𝕓{I} V2.
 #d #e #K1 #I #V1 #L2 #Hd #H @(ltpss_ind … H) -L2
 [ /2 width=5/
-| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L;
+| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct
   elim (ltps_inv_tps11 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H
   lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2
   lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/
 ]
-qed.
+qed-.