matita/matita/contribs/lambdadelta/ground/lib/exteq.ma

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  14
  15 include "ground/notation/relations/doteq_4.ma".
  16 include "ground/lib/relations.ma".
  17
  18 (* EXTENSIONAL EQUIVALENCE **************************************************)
  19
  20 definition exteq (A,B:Type[0]): relation (A → B) ≝
  21                                 λf1,f2. ∀a. f1 a = f2 a.
  22
  23 interpretation "extensional equivalence"
  24    'DotEq A B f1 f2 = (exteq A B f1 f2).
  25
  26 (* Basic_properties *********************************************************)
  27
  28 lemma exteq_refl (A) (B): reflexive … (exteq A B).
  29 // qed.
  30
  31 lemma exteq_repl (A) (B): replace_2 … (exteq A B) (exteq A B) (exteq A B).
  32 // qed-.
  33
  34 lemma exteq_sym (A) (B): symmetric … (exteq A B).
  35 /2 width=1 by exteq_repl/ qed-.
  36
  37 lemma exteq_trans (A) (B): Transitive … (exteq A B).
  38 /2 width=1 by exteq_repl/ qed-.
  39