1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/flt/defs.ma".
19 include "basic_1/C/props.ma".
22 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c u c
25 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(lt_reg_l
26 (tweight u) (S (plus (tweight u) (tweight t))) (cweight c) (le_n_S (tweight
27 u) (plus (tweight u) (tweight t)) (le_plus_l (tweight u) (tweight t))))))).
30 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c t c
33 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(lt_reg_l
34 (tweight t) (S (plus (tweight u) (tweight t))) (cweight c) (le_n_S (tweight
35 t) (plus (tweight u) (tweight t)) (le_plus_r (tweight u) (tweight t))))))).
38 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt (CHead c
39 k u) t c (THead k u t)))))
41 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(eq_ind nat
42 (S (plus (cweight c) (plus (tweight u) (tweight t)))) (\lambda (n: nat).(lt
43 (plus (plus (cweight c) (tweight u)) (tweight t)) n)) (eq_ind_r nat (plus
44 (plus (cweight c) (tweight u)) (tweight t)) (\lambda (n: nat).(lt (plus (plus
45 (cweight c) (tweight u)) (tweight t)) (S n))) (le_n (S (plus (plus (cweight
46 c) (tweight u)) (tweight t)))) (plus (cweight c) (plus (tweight u) (tweight
47 t))) (plus_assoc_l (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S
48 (plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u)
52 \forall (k: K).(\forall (c: C).(\forall (t: T).(\forall (i: nat).(flt c t
53 (CHead c k t) (TLRef i)))))
55 \lambda (_: K).(\lambda (c: C).(\lambda (t: T).(\lambda (_:
56 nat).(lt_x_plus_x_Sy (plus (cweight c) (tweight t)) O)))).
59 \forall (k1: K).(\forall (c1: C).(\forall (c2: C).(\forall (t1: T).((cle
60 (CHead c1 k1 t1) c2) \to (\forall (k2: K).(\forall (t2: T).(\forall (i:
61 nat).(flt c1 t1 (CHead c2 k2 t2) (TLRef i)))))))))
63 \lambda (_: K).(\lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda
64 (H: (le (plus (cweight c1) (tweight t1)) (cweight c2))).(\lambda (_:
65 K).(\lambda (t2: T).(\lambda (_: nat).(le_lt_trans (plus (cweight c1)
66 (tweight t1)) (cweight c2) (plus (plus (cweight c2) (tweight t2)) (S O)) H
67 (eq_ind_r nat (plus (S O) (plus (cweight c2) (tweight t2))) (\lambda (n:
68 nat).(lt (cweight c2) n)) (le_lt_n_Sm (cweight c2) (plus (cweight c2)
69 (tweight t2)) (le_plus_l (cweight c2) (tweight t2))) (plus (plus (cweight c2)
70 (tweight t2)) (S O)) (plus_sym (plus (cweight c2) (tweight t2)) (S
74 \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (i: nat).((flt c1
75 t1 c2 (TLRef i)) \to (\forall (k2: K).(\forall (t2: T).(\forall (j: nat).(flt
76 c1 t1 (CHead c2 k2 t2) (TLRef j)))))))))
78 \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (_: nat).(\lambda
79 (H: (lt (plus (cweight c1) (tweight t1)) (plus (cweight c2) (S O)))).(\lambda
80 (_: K).(\lambda (t2: T).(\lambda (_: nat).(lt_le_trans (plus (cweight c1)
81 (tweight t1)) (plus (cweight c2) (S O)) (plus (plus (cweight c2) (tweight
82 t2)) (S O)) H (le_plus_plus (cweight c2) (plus (cweight c2) (tweight t2)) (S
83 O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))).
86 \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (c3: C).(\forall
87 (u2: T).(\forall (u3: T).((flt c2 u2 c3 u3) \to (flt c1 u2 c3 u3)))))))
89 \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (le (cweight c1) (cweight
90 c2))).(\lambda (c3: C).(\lambda (u2: T).(\lambda (u3: T).(\lambda (H0: (lt
91 (plus (cweight c2) (tweight u2)) (plus (cweight c3) (tweight
92 u3)))).(le_lt_trans (plus (cweight c1) (tweight u2)) (plus (cweight c2)
93 (tweight u2)) (plus (cweight c3) (tweight u3)) (le_plus_plus (cweight c1)
94 (cweight c2) (tweight u2) (tweight u2) H (le_n (tweight u2))) H0))))))).
97 \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).((flt c1
98 t1 c2 t2) \to (\forall (c3: C).(\forall (t3: T).((flt c2 t2 c3 t3) \to (flt
101 \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda
102 (H: (lt (fweight c1 t1) (fweight c2 t2))).(\lambda (c3: C).(\lambda (t3:
103 T).(\lambda (H0: (lt (fweight c2 t2) (fweight c3 t3))).(lt_trans (fweight c1
104 t1) (fweight c2 t2) (fweight c3 t3) H H0)))))))).