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: term → term → Prop ≝
  20    | thom_sort: ∀k. thom (⋆k) (⋆k)
  21    | thom_lref: ∀i. thom (#i) (#i)
  22    | thom_abst: ∀V1,V2,T1,T2. thom (𝕚{Abst} V1. T1) (𝕚{Abst} V2. T2)
  23    | thom_appl: ∀V1,V2,T1,T2. thom T1 T2 → 𝕊[T1] → 𝕊[T2] →
  24                 thom (𝕚{Appl} V1. T1) (𝕚{Appl} V2. T2)
  25 .
  26
  27 interpretation "homomorphic (term)" 'napart T1 T2 = (thom T1 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma thom_sym: ∀T1,T2. T1 ≈ T2 → T2 ≈ T1.
  32 #T1 #T2 #H elim H -H T1 T2 /2/
  33 qed.
  34
  35 lemma thom_refl2: ∀T1,T2. T1 ≈ T2 → T2 ≈ T2.
  36 #T1 #T2 #H elim H -H T1 T2 /2/
  37 qed.
  38
  39 lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
  40 /3/ qed.
  41
  42 lemma simple_thom_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝕊[T1] → 𝕊[T2].
  43 #T1 #T2 #H elim H -H T1 T2 //
  44 #V1 #V2 #T1 #T2 #H
  45 elim (simple_inv_bind … H)
  46 qed.
  47
  48 lemma simple_thom_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝕊[T2] → 𝕊[T1].
  49 /3/ qed.
  50
  51 (* Basic inversion lemmas ***************************************************)