- matitaInit matitaprover matitadep matitamake:

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / Base-1 / preamble.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma
index 1a6874e54204330e3d60c22fa9157d031ad072fc..f5ad380c9d421adc85cbd0164c695836c0b61644 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma
@@ -36,6 +36,7 @@ alias id "False_ind" = "cic:/Coq/Init/Logic/False_ind.con".
 alias id "I" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1/1)".
 alias id "land" = "cic:/Coq/Init/Logic/and.ind#xpointer(1/1)".
 alias id "le" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1)".
+alias id "le_ind" = "cic:/Coq/Init/Peano/le_ind.con".
 alias id "le_lt_n_Sm" = "cic:/Coq/Arith/Lt/le_lt_n_Sm.con".
 alias id "le_lt_or_eq" = "cic:/Coq/Arith/Lt/le_lt_or_eq.con".
 alias id "le_n" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1/1)".
@@ -48,6 +49,7 @@ alias id "le_plus_l" = "cic:/Coq/Arith/Plus/le_plus_l.con".
 alias id "le_plus_minus" = "cic:/Coq/Arith/Minus/le_plus_minus.con".
 alias id "le_plus_minus_r" = "cic:/Coq/Arith/Minus/le_plus_minus_r.con".
 alias id "le_plus_r" = "cic:/Coq/Arith/Plus/le_plus_r.con".
+alias id "le_pred_n" = "cic:/Coq/Arith/Le/le_pred_n.con".
 alias id "le_S" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1/2)".
 alias id "le_S_n" = "cic:/Coq/Arith/Le/le_S_n.con".
 alias id "le_Sn_n" = "cic:/Coq/Arith/Le/le_Sn_n.con".
@@ -97,10 +99,14 @@ theorem sym_not_eq: \forall A:Type. \forall x,y:A. x \neq y \to y \neq x.
  unfold not. intros. apply H. symmetry. assumption.
 qed.
 
+theorem trans_eq : \forall A:Type. \forall x,y,z:A. x=y \to y=z \to x=z.
+ intros. transitivity y; assumption.
+qed.
+
 theorem plus_reg_l: \forall n,m,p. n + m = n + p \to m = p.
- intros. apply plus_reg_l; auto.
+ intros. apply plus_reg_l; autobatch.
 qed.
 
 theorem plus_le_reg_l: \forall p,n,m. p + n <= p + m \to n <= m.
- intros. apply plus_le_reg_l; auto.
+ intros. apply plus_le_reg_l; autobatch.
 qed.