(∀L,L2. L1 [d, e] ≫* L → L [d, e] ≫ L2 → R L → R L2) →
∀L2. L1 [d, e] ≫* L2 → R L2.
#d #e #L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
(∀L,L2. L1 [d, e] ≫* L → L [d, e] ≫ L2 → R L → R L2) →
∀L2. L1 [d, e] ≫* L2 → R L2.
#d #e #L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
lemma ltpss_inv_refl_O2: ∀d,L1,L2. L1 [d, 0] ≫* L2 → L1 = L2.
#d #L1 #L2 #H @(ltpss_ind … H) -L2 //
#L #L2 #_ #HL2 #IHL <(ltps_inv_refl_O2 … HL2) -HL2 //
lemma ltpss_inv_refl_O2: ∀d,L1,L2. L1 [d, 0] ≫* L2 → L1 = L2.
#d #L1 #L2 #H @(ltpss_ind … H) -L2 //
#L #L2 #_ #HL2 #IHL <(ltps_inv_refl_O2 … HL2) -HL2 //
lemma ltpss_inv_atom1: ∀d,e,L2. ⋆ [d, e] ≫* L2 → L2 = ⋆.
#d #e #L2 #H @(ltpss_ind … H) -L2 //
#L #L2 #_ #HL2 #IHL destruct -L
>(ltps_inv_atom1 … HL2) -HL2 //
lemma ltpss_inv_atom1: ∀d,e,L2. ⋆ [d, e] ≫* L2 → L2 = ⋆.
#d #e #L2 #H @(ltpss_ind … H) -L2 //
#L #L2 #_ #HL2 #IHL destruct -L
>(ltps_inv_atom1 … HL2) -HL2 //
fact ltpss_inv_atom2_aux: ∀d,e,L1,L2.
L1 [d, e] ≫* L2 → L2 = ⋆ → L1 = ⋆.
fact ltpss_inv_atom2_aux: ∀d,e,L1,L2.
L1 [d, e] ≫* L2 → L2 = ⋆ → L1 = ⋆.
qed.
lemma ltpss_inv_atom2: ∀d,e,L1. L1 [d, e] ≫* ⋆ → L1 = ⋆.
qed.
lemma ltpss_inv_atom2: ∀d,e,L1. L1 [d, e] ≫* ⋆ → L1 = ⋆.
(*
fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
∀K2,I,V2. L2 = K2. 𝕓{I} V2 →
(*
fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
∀K2,I,V2. L2 = K2. 𝕓{I} V2 →