problems-4 was due to trans_eq expecting an explicit named substitution.

diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/Base/ext/preamble.ma b/matita/contribs/LAMBDA-TYPES/Level-1/Base/ext/preamble.ma
index 3892cb628154ce66eb78ba3434bb38b7e1a59dee..040b878aa0032faecd54e3af1874aceb964bd9a5 100644 (file)
--- a/matita/contribs/LAMBDA-TYPES/Level-1/Base/ext/preamble.ma
+++ b/matita/contribs/LAMBDA-TYPES/Level-1/Base/ext/preamble.ma
@@ -138,6 +138,12 @@ 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 : ∀A:Type.∀x,y,z:A.x=y→y=z→x=z.
+ intros;
+ transitivity y;
+ assumption.
+qed.
+
 theorem plus_reg_l: \forall (n,m,p:nat). n + m = n + p \to m = p.
  intros. apply plus_reg_l; auto.
 qed.
@@ -151,7 +157,7 @@ definition sym_equal \def sym_eq.
 default "equality"
  cic:/Coq/Init/Logic/eq.ind
  cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/sym_eq.con
- cic:/Coq/Init/Logic/trans_eq.con
+ cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/trans_eq.con
  cic:/Coq/Init/Logic/eq_ind.con
  cic:/Coq/Init/Logic/eq_ind_r.con
  cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/f_equal.con

diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/problems-4.ma b/matita/contribs/LAMBDA-TYPES/Level-1/problems-4.ma
deleted file mode 100644 (file)
index 03dfdaf..0000000
--- a/matita/contribs/LAMBDA-TYPES/Level-1/problems-4.ma
+++ /dev/null
@@ -1,96 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* Problematic objects for disambiguation/typechecking ********************)
-
-set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/problems".
-
-include "LambdaDelta/theory.ma".
-
-theorem leq_trans:
- \forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (\forall 
-(a3: A).((leq g a2 a3) \to (leq g a1 a3))))))
-\def
- \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq g a1 
-a2)).(leq_ind g (\lambda (a: A).(\lambda (a0: A).(\forall (a3: A).((leq g a0 
-a3) \to (leq g a a3))))) (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1: 
-nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda (H0: (eq A (aplus g (ASort 
-h1 n1) k) (aplus g (ASort h2 n2) k))).(\lambda (a3: A).(\lambda (H1: (leq g 
-(ASort h2 n2) a3)).(let H2 \def (match H1 in leq return (\lambda (a: 
-A).(\lambda (a0: A).(\lambda (_: (leq ? a a0)).((eq A a (ASort h2 n2)) \to 
-((eq A a0 a3) \to (leq g (ASort h1 n1) a3)))))) with [(leq_sort h0 h3 n0 n3 
-k0 H2) \Rightarrow (\lambda (H3: (eq A (ASort h0 n0) (ASort h2 n2))).(\lambda 
-(H4: (eq A (ASort h3 n3) a3)).((let H5 \def (f_equal A nat (\lambda (e: 
-A).(match e in A return (\lambda (_: A).nat) with [(ASort _ n) \Rightarrow n 
-| (AHead _ _) \Rightarrow n0])) (ASort h0 n0) (ASort h2 n2) H3) in ((let H6 
-\def (f_equal A nat (\lambda (e: A).(match e in A return (\lambda (_: A).nat) 
-with [(ASort n _) \Rightarrow n | (AHead _ _) \Rightarrow h0])) (ASort h0 n0) 
-(ASort h2 n2) H3) in (eq_ind nat h2 (\lambda (n: nat).((eq nat n0 n2) \to 
-((eq A (ASort h3 n3) a3) \to ((eq A (aplus g (ASort n n0) k0) (aplus g (ASort 
-h3 n3) k0)) \to (leq g (ASort h1 n1) a3))))) (\lambda (H7: (eq nat n0 
-n2)).(eq_ind nat n2 (\lambda (n: nat).((eq A (ASort h3 n3) a3) \to ((eq A 
-(aplus g (ASort h2 n) k0) (aplus g (ASort h3 n3) k0)) \to (leq g (ASort h1 
-n1) a3)))) (\lambda (H8: (eq A (ASort h3 n3) a3)).(eq_ind A (ASort h3 n3) 
-(\lambda (a: A).((eq A (aplus g (ASort h2 n2) k0) (aplus g (ASort h3 n3) k0)) 
-\to (leq g (ASort h1 n1) a))) (\lambda (H9: (eq A (aplus g (ASort h2 n2) k0) 
-(aplus g (ASort h3 n3) k0))).(lt_le_e k k0 (leq g (ASort h1 n1) (ASort h3 
-n3)) (\lambda (H10: (lt k k0)).(let H_y \def (aplus_reg_r g (ASort h1 n1) 
-(ASort h2 n2) k k H0 (minus k0 k)) in (let H11 \def (eq_ind_r nat (plus 
-(minus k0 k) k) (\lambda (n: nat).(eq A (aplus g (ASort h1 n1) n) (aplus g 
-(ASort h2 n2) n))) H_y k0 (le_plus_minus_sym k k0 (le_S_n k k0 (le_S (S k) k0 
-H10)))) in (leq_sort g h1 h3 n1 n3 k0 (trans_eq A (aplus g (ASort h1 n1) k0) 
-(aplus g (ASort h2 n2) k0) (aplus g (ASort h3 n3) k0) H11 H9))))) (\lambda 
-(H10: (le k0 k)).(let H_y \def (aplus_reg_r g (ASort h2 n2) (ASort h3 n3) k0 
-k0 H9 (minus k k0)) in (let H11 \def (eq_ind_r nat (plus (minus k k0) k0) 
-(\lambda (n: nat).(eq A (aplus g (ASort h2 n2) n) (aplus g (ASort h3 n3) n))) 
-H_y k (le_plus_minus_sym k0 k H10)) in (leq_sort g h1 h3 n1 n3 k (trans_eq A 
-(aplus g (ASort h1 n1) k) (aplus g (ASort h2 n2) k) (aplus g (ASort h3 n3) k) 
-H0 H11))))))) a3 H8)) n0 (sym_eq nat n0 n2 H7))) h0 (sym_eq nat h0 h2 H6))) 
-H5)) H4 H2))) | (leq_head a0 a4 H2 a5 a6 H3) \Rightarrow (\lambda (H4: (eq A 
-(AHead a0 a5) (ASort h2 n2))).(\lambda (H5: (eq A (AHead a4 a6) a3)).((let H6 
-\def (eq_ind A (AHead a0 a5) (\lambda (e: A).(match e in A return (\lambda 
-(_: A).Prop) with [(ASort _ _) \Rightarrow False | (AHead _ _) \Rightarrow 
-True])) I (ASort h2 n2) H4) in (False_ind ((eq A (AHead a4 a6) a3) \to ((leq 
-g a0 a4) \to ((leq g a5 a6) \to (leq g (ASort h1 n1) a3)))) H6)) H5 H2 
-H3)))]) in (H2 (refl_equal A (ASort h2 n2)) (refl_equal A a3))))))))))) 
-(\lambda (a3: A).(\lambda (a4: A).(\lambda (_: (leq g a3 a4)).(\lambda (H1: 
-((\forall (a5: A).((leq g a4 a5) \to (leq g a3 a5))))).(\lambda (a5: 
-A).(\lambda (a6: A).(\lambda (_: (leq g a5 a6)).(\lambda (H3: ((\forall (a7: 
-A).((leq g a6 a7) \to (leq g a5 a7))))).(\lambda (a0: A).(\lambda (H4: (leq g 
-(AHead a4 a6) a0)).(let H5 \def (match H4 in leq return (\lambda (a: 
-A).(\lambda (a7: A).(\lambda (_: (leq ? a a7)).((eq A a (AHead a4 a6)) \to 
-((eq A a7 a0) \to (leq g (AHead a3 a5) a0)))))) with [(leq_sort h1 h2 n1 n2 k 
-H5) \Rightarrow (\lambda (H6: (eq A (ASort h1 n1) (AHead a4 a6))).(\lambda 
-(H7: (eq A (ASort h2 n2) a0)).((let H8 \def (eq_ind A (ASort h1 n1) (\lambda 
-(e: A).(match e in A return (\lambda (_: A).Prop) with [(ASort _ _) 
-\Rightarrow True | (AHead _ _) \Rightarrow False])) I (AHead a4 a6) H6) in 
-(False_ind ((eq A (ASort h2 n2) a0) \to ((eq A (aplus g (ASort h1 n1) k) 
-(aplus g (ASort h2 n2) k)) \to (leq g (AHead a3 a5) a0))) H8)) H7 H5))) | 
-(leq_head a7 a8 H5 a9 a10 H6) \Rightarrow (\lambda (H7: (eq A (AHead a7 a9) 
-(AHead a4 a6))).(\lambda (H8: (eq A (AHead a8 a10) a0)).((let H9 \def 
-(f_equal A A (\lambda (e: A).(match e in A return (\lambda (_: A).A) with 
-[(ASort _ _) \Rightarrow a9 | (AHead _ a) \Rightarrow a])) (AHead a7 a9) 
-(AHead a4 a6) H7) in ((let H10 \def (f_equal A A (\lambda (e: A).(match e in 
-A return (\lambda (_: A).A) with [(ASort _ _) \Rightarrow a7 | (AHead a _) 
-\Rightarrow a])) (AHead a7 a9) (AHead a4 a6) H7) in (eq_ind A a4 (\lambda (a: 
-A).((eq A a9 a6) \to ((eq A (AHead a8 a10) a0) \to ((leq g a a8) \to ((leq g 
-a9 a10) \to (leq g (AHead a3 a5) a0)))))) (\lambda (H11: (eq A a9 
-a6)).(eq_ind A a6 (\lambda (a: A).((eq A (AHead a8 a10) a0) \to ((leq g a4 
-a8) \to ((leq g a a10) \to (leq g (AHead a3 a5) a0))))) (\lambda (H12: (eq A 
-(AHead a8 a10) a0)).(eq_ind A (AHead a8 a10) (\lambda (a: A).((leq g a4 a8) 
-\to ((leq g a6 a10) \to (leq g (AHead a3 a5) a)))) (\lambda (H13: (leq g a4 
-a8)).(\lambda (H14: (leq g a6 a10)).(leq_head g a3 a8 (H1 a8 H13) a5 a10 (H3 
-a10 H14)))) a0 H12)) a9 (sym_eq A a9 a6 H11))) a7 (sym_eq A a7 a4 H10))) H9)) 
-H8 H5 H6)))]) in (H5 (refl_equal A (AHead a4 a6)) (refl_equal A 
-a0))))))))))))) a1 a2 H)))).