+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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 *)
-(* *)
-(**************************************************************************)
-
-(* This file was automatically generated: do not edit *********************)
-
-include "basic_1/C/fwd.ma".
-
-include "basic_1/T/props.ma".
-
-lemma cle_r:
- \forall (c: C).(cle c c)
-\def
- \lambda (c: C).(C_ind (\lambda (c0: C).(le (cweight c0) (cweight c0)))
-(\lambda (_: nat).(le_O_n O)) (\lambda (c0: C).(\lambda (_: (le (cweight c0)
-(cweight c0))).(\lambda (_: K).(\lambda (t: T).(le_n (plus (cweight c0)
-(tweight t))))))) c).
-
-lemma cle_head:
- \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (u1: T).(\forall
-(u2: T).((tle u1 u2) \to (\forall (k: K).(cle (CHead c1 k u1) (CHead c2 k
-u2))))))))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (le (cweight c1) (cweight
-c2))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H0: (le (tweight u1)
-(tweight u2))).(\lambda (_: K).(le_plus_plus (cweight c1) (cweight c2)
-(tweight u1) (tweight u2) H H0))))))).
-
-lemma cle_trans_head:
- \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (k: K).(\forall
-(u: T).(cle c1 (CHead c2 k u))))))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (le (cweight c1) (cweight
-c2))).(\lambda (_: K).(\lambda (u: T).(le_plus_trans (cweight c1) (cweight
-c2) (tweight u) H))))).
-
-lemma clt_cong:
- \forall (c: C).(\forall (d: C).((clt c d) \to (\forall (k: K).(\forall (t:
-T).(clt (CHead c k t) (CHead d k t))))))
-\def
- \lambda (c: C).(\lambda (d: C).(\lambda (H: (lt (cweight c) (cweight
-d))).(\lambda (_: K).(\lambda (t: T).(lt_reg_r (cweight c) (cweight d)
-(tweight t) H))))).
-
-lemma clt_head:
- \forall (k: K).(\forall (c: C).(\forall (u: T).(clt c (CHead c k u))))
-\def
- \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(eq_ind_r nat (plus (cweight
-c) O) (\lambda (n: nat).(lt n (plus (cweight c) (tweight u)))) (lt_reg_l O
-(tweight u) (cweight c) (tweight_lt u)) (cweight c) (plus_n_O (cweight c))))).
-
-lemma chead_ctail:
- \forall (c: C).(\forall (t: T).(\forall (k: K).(ex_3 K C T (\lambda (h:
-K).(\lambda (d: C).(\lambda (u: T).(eq C (CHead c k t) (CTail h u d))))))))
-\def
- \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (t: T).(\forall (k: K).(ex_3
-K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C (CHead c0 k t)
-(CTail h u d))))))))) (\lambda (n: nat).(\lambda (t: T).(\lambda (k:
-K).(ex_3_intro K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C
-(CHead (CSort n) k t) (CTail h u d))))) k (CSort n) t (refl_equal C (CHead
-(CSort n) k t)))))) (\lambda (c0: C).(\lambda (H: ((\forall (t: T).(\forall
-(k: K).(ex_3 K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C
-(CHead c0 k t) (CTail h u d)))))))))).(\lambda (k: K).(\lambda (t:
-T).(\lambda (t0: T).(\lambda (k0: K).(let H_x \def (H t k) in (let H0 \def
-H_x in (ex_3_ind K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C
-(CHead c0 k t) (CTail h u d))))) (ex_3 K C T (\lambda (h: K).(\lambda (d:
-C).(\lambda (u: T).(eq C (CHead (CHead c0 k t) k0 t0) (CTail h u d))))))
-(\lambda (x0: K).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H1: (eq C (CHead
-c0 k t) (CTail x0 x2 x1))).(eq_ind_r C (CTail x0 x2 x1) (\lambda (c1:
-C).(ex_3 K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C (CHead
-c1 k0 t0) (CTail h u d))))))) (ex_3_intro K C T (\lambda (h: K).(\lambda (d:
-C).(\lambda (u: T).(eq C (CHead (CTail x0 x2 x1) k0 t0) (CTail h u d))))) x0
-(CHead x1 k0 t0) x2 (refl_equal C (CHead (CTail x0 x2 x1) k0 t0))) (CHead c0
-k t) H1))))) H0))))))))) c).
-
-lemma clt_thead:
- \forall (k: K).(\forall (u: T).(\forall (c: C).(clt c (CTail k u c))))
-\def
- \lambda (k: K).(\lambda (u: T).(\lambda (c: C).(C_ind (\lambda (c0: C).(clt
-c0 (CTail k u c0))) (\lambda (n: nat).(clt_head k (CSort n) u)) (\lambda (c0:
-C).(\lambda (H: (clt c0 (CTail k u c0))).(\lambda (k0: K).(\lambda (t:
-T).(clt_cong c0 (CTail k u c0) H k0 t))))) c))).
-
-lemma c_tail_ind:
- \forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to
-(((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CTail k t
-c))))))) \to (\forall (c: C).(P c))))
-\def
- \lambda (P: ((C \to Prop))).(\lambda (H: ((\forall (n: nat).(P (CSort
-n))))).(\lambda (H0: ((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t:
-T).(P (CTail k t c)))))))).(\lambda (c: C).(clt_wf_ind (\lambda (c0: C).(P
-c0)) (\lambda (c0: C).(C_ind (\lambda (c1: C).(((\forall (d: C).((clt d c1)
-\to (P d)))) \to (P c1))) (\lambda (n: nat).(\lambda (_: ((\forall (d:
-C).((clt d (CSort n)) \to (P d))))).(H n))) (\lambda (c1: C).(\lambda (_:
-((((\forall (d: C).((clt d c1) \to (P d)))) \to (P c1)))).(\lambda (k:
-K).(\lambda (t: T).(\lambda (H2: ((\forall (d: C).((clt d (CHead c1 k t)) \to
-(P d))))).(let H_x \def (chead_ctail c1 t k) in (let H3 \def H_x in (ex_3_ind
-K C T (\lambda (h: K).(\lambda (d: C).(\lambda (u: T).(eq C (CHead c1 k t)
-(CTail h u d))))) (P (CHead c1 k t)) (\lambda (x0: K).(\lambda (x1:
-C).(\lambda (x2: T).(\lambda (H4: (eq C (CHead c1 k t) (CTail x0 x2
-x1))).(eq_ind_r C (CTail x0 x2 x1) (\lambda (c2: C).(P c2)) (let H5 \def
-(eq_ind C (CHead c1 k t) (\lambda (c2: C).(\forall (d: C).((clt d c2) \to (P
-d)))) H2 (CTail x0 x2 x1) H4) in (H0 x1 (H5 x1 (clt_thead x0 x2 x1)) x0 x2))
-(CHead c1 k t) H4))))) H3)))))))) c0)) c)))).
-
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