(* Advanced properties ******************************************************)
-(* Basic_2A1: uses: fpbs_intro_alt *)
-lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
- ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
- ∀L0. ⦃G, L⦄ ⊢ ⬈*[h, T0] L0 →
- ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
+lemma fpbs_intro_fstar: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+ ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
+ ∀L0. ⦃G, L⦄ ⊢ ⬈*[h, T0] L0 →
+ ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
/3 width=5 by cpxs_fqus_lfpxs_fpbs, fpbs_strap1, fpbq_ffdeq/ qed.
(* Advanced inversion lemmas *************************************************)
-(* Basic_2A1: uses: fpbs_inv_alt *)
-lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
- ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
- & ⦃G, L⦄ ⊢ ⬈*[h, T0] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+lemma fpbs_inv_fstar: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
+ ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
+ & ⦃G, L⦄ ⊢ ⬈*[h, T0] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
[ /2 width=9 by ex4_5_intro/
| #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0