lemma ltpss_tpss2: ∀L1,L2,I,V1,V2,e.
L1 [0, e] ▶* L2 → L2 ⊢ V1 [0, e] ▶* V2 →
lemma ltpss_tpss2: ∀L1,L2,I,V1,V2,e.
L1 [0, e] ▶* L2 → L2 ⊢ V1 [0, e] ▶* V2 →
#L1 #L2 #I #V1 #V2 #e #HL12 #H @(tpss_ind … H) -V2
[ /2 width=1/
| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
#L1 #L2 #I #V1 #V2 #e #HL12 #H @(tpss_ind … H) -V2
[ /2 width=1/
| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
lemma ltpss_tpss2_lt: ∀L1,L2,I,V1,V2,e.
L1 [0, e - 1] ▶* L2 → L2 ⊢ V1 [0, e - 1] ▶* V2 →
lemma ltpss_tpss2_lt: ∀L1,L2,I,V1,V2,e.
L1 [0, e - 1] ▶* L2 → L2 ⊢ V1 [0, e - 1] ▶* V2 →
#L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
>(plus_minus_m_m e 1) // /2 width=1/
qed.
lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
L1 [d, e] ▶* L2 → L2 ⊢ V1 [d, e] ▶* V2 →
#L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
>(plus_minus_m_m e 1) // /2 width=1/
qed.
lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
L1 [d, e] ▶* L2 → L2 ⊢ V1 [d, e] ▶* V2 →
#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2
[ /2 width=1/
| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2
[ /2 width=1/
| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
lemma ltpss_tpss1_lt: ∀L1,L2,I,V1,V2,d,e.
L1 [d - 1, e] ▶* L2 → L2 ⊢ V1 [d - 1, e] ▶* V2 →
lemma ltpss_tpss1_lt: ∀L1,L2,I,V1,V2,d,e.
L1 [d - 1, e] ▶* L2 → L2 ⊢ V1 [d - 1, e] ▶* V2 →