(* Advanced properties ******************************************************)
-lemma fsle_lifts_sn: â\88\80T1,U1. â¬\86*[1] T1 â\89¡ U1 → ∀L1,L2. |L2| ≤ |L1| →
+lemma fsle_lifts_sn: â\88\80T1,U1. â¬\86*[1] T1 â\89\98 U1 → ∀L1,L2. |L2| ≤ |L1| →
∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄.
#T1 #U1 #HTU1 #L1 #L2 #H1L #T2
* #n #m #f #g #Hf #Hg #H2L #Hfg
qed-.
lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
- â\88\80W1. â¬\86*[1] V1 â\89¡ W1 → ∀I1,I2. ⦃K1.ⓘ{I1}, W1⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
+ â\88\80W1. â¬\86*[1] V1 â\89\98 W1 → ∀I1,I2. ⦃K1.ⓘ{I1}, W1⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
#K1 #K2 #HK #V1 #V2
* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
#W1 #HVW1 #I1 #I2
qed.
lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ⦃K1, T1⦄ ⊆ ⦃K2, T2⦄ →
- â\88\80U1,U2. â¬\86*[1] T1 â\89¡ U1 â\86\92 â¬\86*[1] T2 â\89¡ U2 →
+ â\88\80U1,U2. â¬\86*[1] T1 â\89\98 U1 â\86\92 â¬\86*[1] T2 â\89\98 U2 →
∀I1,I2. ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄.
#K1 #K2 #HK #T1 #T2
* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
(* Advanced inversion lemmas ************************************************)
-lemma fsle_inv_lifts_sn: â\88\80T1,U1. â¬\86*[1] T1 â\89¡ U1 →
+lemma fsle_inv_lifts_sn: â\88\80T1,U1. â¬\86*[1] T1 â\89\98 U1 →
∀I1,I2,L1,L2,V1,V2,U2. ⦃L1.ⓑ{I1}V1,U1⦄ ⊆ ⦃L2.ⓑ{I2}V2, U2⦄ →
∀p. ⦃L1, T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.U2⦄.
#T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2