/2 width=1/ qed.
(* Note: new property *)
-(* Basic_1: was only: pr2_thin_dx *)
+(* Basic_1: was only: pr2_thin_dx *)
lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
L ⊢ V1 ➡ V2 → L ⊢ T1 ➡ T2 → L ⊢ ⓕ{I} V1. T1 ➡ ⓕ{I} V2. T2.
#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/
(* Basic_1: was only: pr2_change *)
lemma cpr_lsubs_trans: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
∀L2. L2 ≼ [0, |L1|] L1 → L2 ⊢ T1 ➡ T2.
-#L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12
+#L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12
lapply (tpss_lsubs_trans … HT2 … HL12) -HT2 -HL12 /3 width=4/
qed.
(* Basic forward lemmas *****************************************************)
+lemma cpr_fwd_bind1_minus: ∀I,L,V1,T1,T. L ⊢ -ⓑ{I}V1.T1 ➡ T → ∀b.
+ ∃∃V2,T2. L ⊢ ⓑ{b,I}V1.T1 ➡ ⓑ{b,I}V2.T2 &
+ T = -ⓑ{I}V2.T2.
+#I #L #V1 #T1 #T * #X #H1 #H2 #b
+elim (tpr_fwd_bind1_minus … H1 b) -H1 #V0 #T0 #HT10 #H destruct
+elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV02 #HT02 #H destruct /4 width=5/
+qed-.
+
lemma cpr_fwd_shift1: ∀L,L1,T1,T. L ⊢ L1 @@ T1 ➡ T →
∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
#L #L1 #T1 #T * #X #H1 #H2
elim (tpss_fwd_shift1 … H2) -H2 #L2 #T2 #HL02 #H destruct /2 width=4/
qed-.
-(* Basic_1: removed theorems 6:
+(* Basic_1: removed theorems 6:
pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
pr2_gen_ctail pr2_ctail
Basic_1: removed local theorems 3: