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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "Basic-2/grammar/term_simple.ma".
17 (* HOMOMORPHIC TERMS ********************************************************)
19 inductive thom: term → term → Prop ≝
20 | thom_atom: ∀I. thom (𝕒{I}) (𝕒{I})
21 | thom_abst: ∀V1,V2,T1,T2. thom (𝕔{Abst} V1. T1) (𝕔{Abst} V2. T2)
22 | thom_appl: ∀V1,V2,T1,T2. thom T1 T2 → 𝕊[T1] → 𝕊[T2] →
23 thom (𝕔{Appl} V1. T1) (𝕔{Appl} V2. T2)
26 interpretation "homomorphic (term)" 'napart T1 T2 = (thom T1 T2).
28 (* Basic properties *********************************************************)
30 lemma thom_sym: ∀T1,T2. T1 ≈ T2 → T2 ≈ T1.
31 #T1 #T2 #H elim H -H T1 T2 /2/
34 lemma thom_refl2: ∀T1,T2. T1 ≈ T2 → T2 ≈ T2.
35 #T1 #T2 #H elim H -H T1 T2 /2/
38 lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
41 lemma simple_thom_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝕊[T1] → 𝕊[T2].
42 #T1 #T2 #H elim H -H T1 T2 //
44 elim (simple_inv_bind … H)
47 lemma simple_thom_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝕊[T2] → 𝕊[T1].
50 (* Basic inversion lemmas ***************************************************)
53 (* Basic-1: removed theorems 7:
54 iso_gen_sort iso_gen_lref iso_gen_head iso_refl iso_trans
55 iso_flats_lref_bind_false iso_flats_flat_bind_false