freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / num / bool_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma
index 241ee867562d49ba33e1e7e0479fc61d04b5c170..b7b9096e871706bddcb98a46ce4b85db2221168c 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/bool_lemmas.ma
@@ -130,6 +130,13 @@ nlemma decidable_bool : ∀x,y:bool.decidable (x = y).
  ##]
 nqed.
 
+nlemma decidable_bexpr : ∀x.(x = true) ∨ (x = false).
+ #x; ncases x;
+ ##[ ##1: napply (or2_intro1 (true = true) (true = false) (refl_eq …))
+ ##| ##2: napply (or2_intro2 (false = true) (false = false) (refl_eq …))
+ ##]
+nqed.
+
 nlemma neqbool_to_neq : ∀b1,b2:bool.(eq_bool b1 b2 = false) → (b1 ≠ b2).
  #b1; #b2;
  ncases b1;
@@ -150,6 +157,34 @@ nlemma neq_to_neqbool : ∀b1,b2.b1 ≠ b2 → eq_bool b1 b2 = false.
  ##]
 nqed.
 
+nlemma eqfalse_to_neqtrue : ∀x.x = false → x ≠ true.
+ #x; nelim x;
+ ##[ ##1: #H; napply (bool_destruct … H)
+ ##| ##2: #H; nnormalize; #H1; napply (bool_destruct … H1)
+ ##]
+nqed.
+
+nlemma eqtrue_to_neqfalse : ∀x.x = true → x ≠ false.
+ #x; nelim x;
+ ##[ ##1: #H; nnormalize; #H1; napply (bool_destruct … H1)
+ ##| ##2: #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma neqfalse_to_eqtrue : ∀x.x ≠ false → x = true.
+ #x; nelim x;
+ ##[ ##1: #H; napply refl_eq
+ ##| ##2: nnormalize; #H; nelim (H (refl_eq …))
+ ##]
+nqed.
+
+nlemma neqtrue_to_eqfalse : ∀x.x ≠ true → x = false.
+ #x; nelim x;
+ ##[ ##1: nnormalize; #H; nelim (H (refl_eq …))
+ ##| ##2: #H; napply refl_eq
+ ##]
+nqed.
+
 nlemma andb_true_true_l: ∀b1,b2.(b1 ⊗ b2) = true → b1 = true.
  #b1; #b2;
  ncases b1;