milestone update in basic_2, update in ground and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpm_conf.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
index d8c2d4e26d7491b77b4d1d8d7a54d90d6748b7d6..3ef5de466273fa4774a2cfdf073373ed2302fd6d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
@@ -32,7 +32,7 @@ fact cnv_cpm_conf_lpr_atom_ess_aux (h) (G) (L1) (L2) (s):
 /3 width=3 by cpm_cpms, ex2_intro/ qed-.
 
 fact cnv_cpm_conf_lpr_atom_delta_aux (h) (a) (G) (L) (i):
-     (∀G0,L0,T0. ❪G,L,#i❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,#i❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫⊢#i![h,a] →
      ∀K,V. ⇩[i]L ≘ K.ⓓV →
      ∀n,XV. ❪G,K❫ ⊢ V ➡[h,n] XV →
@@ -54,7 +54,7 @@ elim (cpms_lifts_sn … HVX … HLK2 … HXV) -XV -HLK2 #XV #HVX #HXV
 qed-.
 
 fact cnv_cpm_conf_lpr_atom_ell_aux (h) (a) (G) (L) (i):
-     (∀G0,L0,T0. ❪G,L,#i❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,#i❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫⊢#i![h,a] →
      ∀K,W. ⇩[i]L ≘ K.ⓛW →
      ∀n,XW. ❪G,K❫ ⊢ W ➡[h,n] XW →
@@ -76,7 +76,7 @@ elim (cpms_lifts_sn … HWX … HLK2 … HXW) -XW -HLK2 #XW #HWX #HXW
 qed-.
 
 fact cnv_cpm_conf_lpr_delta_delta_aux (h) (a) (I) (G) (L) (i):
-     (∀G0,L0,T0. ❪G,L,#i❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,#i❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫⊢#i![h,a] →
      ∀K1,V1. ⇩[i]L ≘ K1.ⓑ[I]V1 → ∀K2,V2. ⇩[i]L ≘ K2.ⓑ[I]V2 →
      ∀n1,XV1. ❪G,K1❫ ⊢ V1 ➡[h,n1] XV1 → ∀n2,XV2. ❪G,K2❫ ⊢ V2 ➡[h,n2] XV2 →
@@ -108,7 +108,7 @@ lapply (drops_mono … HLK2 … HLK1) -L -i #H destruct
 qed-.
 
 fact cnv_cpm_conf_lpr_bind_bind_aux (h) (a) (p) (I) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓑ[p,I]V.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓑ[p,I]V.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓑ[p,I]V.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀n1,T1. ❪G,L.ⓑ[I]V❫ ⊢ T ➡[h,n1] T1 → ∀n2,T2. ❪G,L.ⓑ[I]V❫ ⊢ T ➡[h,n2] T2 →
@@ -125,7 +125,7 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓑ[I]V1) … (L2.ⓑ[I]
 qed-.
 
 fact cnv_cpm_conf_lpr_bind_zeta_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,+ⓓV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,+ⓓV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ +ⓓV.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢V ➡[h,0] V1 → ∀n1,T1. ❪G,L.ⓓV❫ ⊢ T ➡[h,n1] T1 →
      ∀T2. ⇧[1]T2 ≘ T → ∀n2,XT2. ❪G,L❫ ⊢ T2 ➡[h,n2] XT2 →
@@ -145,7 +145,7 @@ elim (cnv_cpm_conf_lpr_sub … IH … HXT12 … HXT2 … HL01 … HL02)
 qed-.
 
 fact cnv_cpm_conf_lpr_zeta_zeta_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,+ⓓV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,+ⓓV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ +ⓓV.T ![h,a] →
      ∀T1. ⇧[1]T1 ≘ T → ∀T2. ⇧[1]T2 ≘ T →
      ∀n1,XT1. ❪G,L❫ ⊢ T1 ➡[h,n1] XT1 → ∀n2,XT2. ❪G,L❫ ⊢ T2 ➡[h,n2] XT2 →
@@ -164,7 +164,7 @@ elim (cnv_cpm_conf_lpr_sub … IH … HXT1 … HXT2 … HL01 … HL02)
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_appl_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓐV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓐV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓐV.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀n1,T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 → ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
@@ -181,7 +181,7 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (∀G0,L0,T0. ❪G,L,ⓐV.ⓛ[p]W.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓐV.ⓛ[p]W.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀W2. ❪G,L❫ ⊢ W ➡[h,0] W2 →
@@ -203,7 +203,7 @@ lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 [ /2 width=1 by lsubr_
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (∀G0,L0,T0. ❪G,L,ⓐV.ⓓ[p]W.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓐV.ⓓ[p]W.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀W2. ❪G,L❫ ⊢ W ➡[h,0] W2 →
@@ -234,7 +234,7 @@ elim (cpm_inv_abbr1 … HX) -HX *
 qed-.
 
 fact cnv_cpm_conf_lpr_beta_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (∀G0,L0,T0. ❪G,L,ⓐV.ⓛ[p]W.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓐV.ⓛ[p]W.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀W1. ❪G,L❫ ⊢ W ➡[h,0] W1 → ∀W2. ❪G,L❫ ⊢ W ➡[h,0] W2 →
@@ -256,7 +256,7 @@ lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_be
 qed-.
 
 fact cnv_cpm_conf_lpr_theta_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (∀G0,L0,T0. ❪G,L,ⓐV.ⓓ[p]W.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓐV.ⓓ[p]W.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
      ∀V1. ❪G,L❫ ⊢ V ➡[h,0] V1 → ∀V2. ❪G,L❫ ⊢ V ➡[h,0] V2 →
      ∀W1. ❪G,L❫ ⊢ W ➡[h,0] W1 → ∀W2. ❪G,L❫ ⊢ W ➡[h,0] W2 →
@@ -279,7 +279,7 @@ lapply (cpm_lifts_bi … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2 … HVU) -V2 -V [ /3
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_cast_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,V1. ❪G,L❫ ⊢ V ➡[h,n1] V1 → ∀n2,V2. ❪G,L❫ ⊢ V ➡[h,n2] V2 →
      ∀T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 → ∀T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
@@ -296,7 +296,7 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_epsilon_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,V1. ❪G,L❫ ⊢ V ➡[h,n1] V1 →
      ∀T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 → ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
@@ -312,8 +312,8 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_ee_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,V1. ❪G,L❫ ⊢ V ➡[h,n1] V1 → ∀n2,V2. ❪G,L❫ ⊢ V ➡[h,n2] V2 →
      ∀T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 →
@@ -327,7 +327,7 @@ lapply (cnv_cpms_trans_lpr_sub … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by f
 elim (cnv_cpms_strip_lpr_sub … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
 elim (cnv_cpms_strip_lpr_sub … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
 -HV02 -HTX0 -HT01 <minus_O_n <minus_n_O #T #HT2 #HT1 #V #HV1 #HV2
-elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ]
+elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=5 by fqup_cpms_fwd_fpbg/ ]
 -L0 -V0 -T0 -X0 #U #HVU #HTU
 lapply (cpms_trans … HV2 … HVU) -V <plus_O_n >minus_plus #H2
 lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
@@ -335,7 +335,7 @@ lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
 qed-.
 
 fact cnv_cpm_conf_lpr_epsilon_epsilon_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 → ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
      ∀L1. ❪G,L❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 →
@@ -350,8 +350,8 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_epsilon_ee_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,T1. ❪G,L❫ ⊢ T ➡[h,n1] T1 → ∀n2,V2. ❪G,L❫ ⊢ V ➡[h,n2] V2 →
      ∀L1. ❪G,L❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 →
@@ -364,7 +364,7 @@ lapply (cnv_cpms_trans_lpr_sub … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by f
 elim (cnv_cpms_strip_lpr_sub … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
 elim (cnv_cpms_strip_lpr_sub … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
 -HV02 -HTX0 -HT01 <minus_O_n <minus_n_O #T #HT2 #HT1 #V #HV1 #HV2
-elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ]
+elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=5 by fqup_cpms_fwd_fpbg/ ]
 -L0 -V0 -T0 -X0 #U #HVU #HTU
 lapply (cpms_trans … HV2 … HVU) -V <plus_O_n >minus_plus #H2
 lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
@@ -372,7 +372,7 @@ lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
 qed-.
 
 fact cnv_cpm_conf_lpr_ee_ee_aux (h) (a) (G) (L) (V) (T):
-     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ >[h] ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     (∀G0,L0,T0. ❪G,L,ⓝV.T❫ > ❪G0,L0,T0❫ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ❪G,L❫ ⊢ ⓝV.T ![h,a] →
      ∀n1,V1. ❪G,L❫ ⊢ V ➡[h,n1] V1 → ∀n2,V2. ❪G,L❫ ⊢ V ➡[h,n2] V2 →
      ∀L1. ❪G,L❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 →
@@ -388,8 +388,8 @@ qed-.
 
 fact cnv_cpm_conf_lpr_aux (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
-     (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
      ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
 #h #a #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
 [ #I #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct