matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma

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  14
  15 include "Basic_2/grammar/term_simple.ma".
  16
  17 (* HOMOMORPHIC TERMS ********************************************************)
  18
  19 inductive thom: relation term ≝
  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)
  24 .
  25
  26 interpretation "homomorphic (term)" 'napart T1 T2 = (thom T1 T2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma thom_sym: ∀T1,T2. T1 ≈ T2 → T2 ≈ T1.
  31 #T1 #T2 #H elim H -H T1 T2 /2/
  32 qed.
  33
  34 lemma thom_refl2: ∀T1,T2. T1 ≈ T2 → T2 ≈ T2.
  35 #T1 #T2 #H elim H -H T1 T2 /2/
  36 qed.
  37
  38 lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
  39 /3/ qed.
  40
  41 lemma simple_thom_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝕊[T1] → 𝕊[T2].
  42 #T1 #T2 #H elim H -H T1 T2 //
  43 #V1 #V2 #T1 #T2 #H
  44 elim (simple_inv_bind … H)
  45 qed. (**) (* remove from index *)
  46
  47 lemma simple_thom_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝕊[T2] → 𝕊[T1].
  48 /3/ qed-.
  49
  50 (* Basic inversion lemmas ***************************************************)
  51
  52
  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
  56 *)