qed.
lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
L1 [d, e] ≫* L2 → L2 ⊢ V1 [d, e] ≫* V2 →
L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2
qed.
lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
L1 [d, e] ≫* L2 → L2 ⊢ V1 [d, e] ≫* V2 →
L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2