(* Main properties **********************************************************)
theorem ltpss_trans_eq: ∀L1,L,L2,d,e.
- L1 [d, e] â\89«* L â\86\92 L [d, e] â\89«* L2 â\86\92 L1 [d, e] â\89«* L2.
-/2/ qed.
+ L1 [d, e] â\96¶* L â\86\92 L [d, e] â\96¶* L2 â\86\92 L1 [d, e] â\96¶* L2.
+/2 width=3/ qed.
lemma ltpss_tpss2: ∀L1,L2,I,V1,V2,e.
- L1 [0, e] â\89«* L2 â\86\92 L2 â\8a¢ V1 [0, e] â\89«* V2 →
- L1. 𝕓{I} V1 [0, e + 1] ≫* L2. 𝕓{I} V2.
+ L1 [0, e] â\96¶* L2 â\86\92 L2 â\8a¢ V1 [0, e] â\96¶* V2 →
+ L1. ⓑ{I} V1 [0, e + 1] ▶* L2. ⓑ{I} V2.
#L1 #L2 #I #V1 #V2 #e #HL12 #H @(tpss_ind … H) -V2
-[ /2/
-| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2/
+[ /2 width=1/
+| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
]
qed.
lemma ltpss_tpss2_lt: ∀L1,L2,I,V1,V2,e.
- L1 [0, e - 1] â\89«* L2 â\86\92 L2 â\8a¢ V1 [0, e - 1] â\89«* V2 →
- 0 < e → L1. 𝕓{I} V1 [0, e] ≫* L2. 𝕓{I} V2.
+ L1 [0, e - 1] â\96¶* L2 â\86\92 L2 â\8a¢ V1 [0, e - 1] â\96¶* V2 →
+ 0 < e → L1. ⓑ{I} V1 [0, e] ▶* L2. ⓑ{I} V2.
#L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
->(plus_minus_m_m e 1) /2/
+>(plus_minus_m_m e 1) // /2 width=1/
qed.
lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
- L1 [d, e] â\89«* L2 â\86\92 L2 â\8a¢ V1 [d, e] â\89«* V2 →
- L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
+ L1 [d, e] â\96¶* L2 â\86\92 L2 â\8a¢ V1 [d, e] â\96¶* V2 →
+ L1. ⓑ{I} V1 [d + 1, e] ▶* L2. ⓑ{I} V2.
#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2
-[ /2/
-| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2/
+[ /2 width=1/
+| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2 width=1/
]
qed.
lemma ltpss_tpss1_lt: ∀L1,L2,I,V1,V2,d,e.
- L1 [d - 1, e] â\89«* L2 â\86\92 L2 â\8a¢ V1 [d - 1, e] â\89«* V2 →
- 0 < d → L1. 𝕓{I} V1 [d, e] ≫* L2. 𝕓{I} V2.
+ L1 [d - 1, e] â\96¶* L2 â\86\92 L2 â\8a¢ V1 [d - 1, e] â\96¶* V2 →
+ 0 < d → L1. ⓑ{I} V1 [d, e] ▶* L2. ⓑ{I} V2.
#L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd
->(plus_minus_m_m d 1) /2/
+>(plus_minus_m_m d 1) // /2 width=1/
qed.