lemma aaa_teqg_conf_reqg (S) (G):
reflexive … S →
- â\88\80L1,T1,A. â\9dªG,L1â\9d« ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 →
- â\88\80L2. L1 â\89\9b[S,T1] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T2 ⁝ A.
+ â\88\80L1,T1,A. â\9d¨G,L1â\9d© ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 →
+ â\88\80L2. L1 â\89\9b[S,T1] L2 â\86\92 â\9d¨G,L2â\9d© ⊢ T2 ⁝ A.
#S #G #HS #L1 #T1 #A #H elim H -G -L1 -T1 -A
[ #G #L1 #s1 #X #H1 elim (teqg_inv_sort1 … H1) -H1 //
| #I #G #L1 #V1 #B #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
lemma aaa_teqg_conf (S) (G) (L) (A):
reflexive … S →
- â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 â\81\9d A â\86\92 â\88\80T2. T1 â\89\9b[S] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 ⁝ A.
+ â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T1 â\81\9d A â\86\92 â\88\80T2. T1 â\89\9b[S] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T2 ⁝ A.
/3 width=7 by aaa_teqg_conf_reqg, reqg_refl/ qed-.
lemma aaa_reqg_conf (S) (G) (T) (A):
reflexive … S →
- â\88\80L1. â\9dªG,L1â\9d« â\8a¢ T â\81\9d A â\86\92 â\88\80L2. L1 â\89\9b[S,T] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T ⁝ A.
+ â\88\80L1. â\9d¨G,L1â\9d© â\8a¢ T â\81\9d A â\86\92 â\88\80L2. L1 â\89\9b[S,T] L2 â\86\92 â\9d¨G,L2â\9d© ⊢ T ⁝ A.
/3 width=7 by aaa_teqg_conf_reqg, teqg_refl/ qed-.