inductive thom: relation term ≝
| thom_atom: ∀I. thom (⓪{I}) (⓪{I})
| thom_abst: ∀V1,V2,T1,T2. thom (ⓛV1. T1) (ⓛV2. T2)
- | thom_appl: â\88\80V1,V2,T1,T2. thom T1 T2 â\86\92 ð\9d\95\8a[T1] â\86\92 ð\9d\95\8a[T2] →
+ | thom_appl: â\88\80V1,V2,T1,T2. thom T1 T2 â\86\92 ð\9d\90\92[T1] â\86\92 ð\9d\90\92[T2] →
thom (ⓐV1. T1) (ⓐV2. T2)
.
lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
/3 width=2/ qed.
-lemma simple_thom_repl_dx: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\95\8a[T1] â\86\92 ð\9d\95\8a[T2].
+lemma simple_thom_repl_dx: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\90\92[T1] â\86\92 ð\9d\90\92[T2].
#T1 #T2 #H elim H -T1 -T2 //
#V1 #V2 #T1 #T2 #H
elim (simple_inv_bind … H)
qed. (**) (* remove from index *)
-lemma simple_thom_repl_sn: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\95\8a[T2] â\86\92 ð\9d\95\8a[T1].
+lemma simple_thom_repl_sn: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\90\92[T2] â\86\92 ð\9d\90\92[T1].
/3 width=3/ qed-.
(* Basic inversion lemmas ***************************************************)
/2 width=5/ qed-.
fact thom_inv_flat1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = ⓕ{I}W1.U1 →
- â\88\83â\88\83W2,U2. U1 â\89\88 U2 & ð\9d\95\8a[U1] & ð\9d\95\8a[U2] &
+ â\88\83â\88\83W2,U2. U1 â\89\88 U2 & ð\9d\90\92[U1] & ð\9d\90\92[U2] &
I = Appl & T2 = ⓐW2. U2.
#T1 #T2 * -T1 -T2
[ #J #I #W1 #U1 #H destruct
qed.
lemma thom_inv_flat1: ∀I,W1,U1,T2. ⓕ{I}W1.U1 ≈ T2 →
- â\88\83â\88\83W2,U2. U1 â\89\88 U2 & ð\9d\95\8a[U1] & ð\9d\95\8a[U2] &
+ â\88\83â\88\83W2,U2. U1 â\89\88 U2 & ð\9d\90\92[U1] & ð\9d\90\92[U2] &
I = Appl & T2 = ⓐW2. U2.
/2 width=4/ qed-.
-
-(* Basic_1: removed theorems 7:
- iso_gen_sort iso_gen_lref iso_gen_head iso_refl iso_trans
- iso_flats_lref_bind_false iso_flats_flat_bind_false
-*)