Theory Lemmas

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theory Lemmas
imports Main
uses [Lemmas.ML]
begin

(*  Title:      HOLCF/IOA/ABP/Lemmas.thy
    ID:         $Id: Lemmas.thy,v 1.7 2005/09/03 14:50:23 wenzelm Exp $
    Author:     Olaf Müller
*)

theory Lemmas
imports Main
begin

end

theorem and_de_morgan_and_absorbe:

  (¬ (AB)) = (¬ AB ∨ ¬ B)

theorem bool_if_impl_or:

  (if C then A else B) --> AB

theorem exis_elim:

  (∃x. x = PQ x) = Q P

theorem singleton_set:

  (UN b. {x. x = f b}) = (UN b. {f b})

theorem de_morgan:

  ((AB) = False) = (¬ A ∧ ¬ B)

theorem hd_append:

  hd (l @ m) = (if l ≠ [] then hd l else hd m)

theorem cons_not_nil:

  l ≠ [] --> (∃x xs. l = x # xs)