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 *********************)
19 include "flt/defs.ma".
24 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c u c
27 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t:
28 T).(plus_le_lt_compat (cweight c) (cweight c) (tweight u) (S (plus (tweight
29 u) (tweight t))) (le_n (cweight c)) (le_n_S (tweight u) (plus (tweight u)
30 (tweight t)) (le_plus_l (tweight u) (tweight t))))))).
33 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c t c
36 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t:
37 T).(plus_le_lt_compat (cweight c) (cweight c) (tweight t) (S (plus (tweight
38 u) (tweight t))) (le_n (cweight c)) (le_n_S (tweight t) (plus (tweight u)
39 (tweight t)) (le_plus_r (tweight u) (tweight t))))))).
42 \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt (CHead c
43 k u) t c (THead k u t)))))
45 \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(eq_ind nat
46 (S (plus (cweight c) (plus (tweight u) (tweight t)))) (\lambda (n: nat).(lt
47 (plus (plus (cweight c) (tweight u)) (tweight t)) n)) (eq_ind_r nat (plus
48 (plus (cweight c) (tweight u)) (tweight t)) (\lambda (n: nat).(lt (plus (plus
49 (cweight c) (tweight u)) (tweight t)) (S n))) (le_n (S (plus (plus (cweight
50 c) (tweight u)) (tweight t)))) (plus (cweight c) (plus (tweight u) (tweight
51 t))) (plus_assoc (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S
52 (plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u)
56 \forall (k: K).(\forall (c: C).(\forall (t: T).(\forall (i: nat).(flt c t
57 (CHead c k t) (TLRef i)))))
59 \lambda (_: K).(\lambda (c: C).(\lambda (t: T).(\lambda (_:
60 nat).(lt_x_plus_x_Sy (plus (cweight c) (tweight t)) O)))).
63 \forall (k1: K).(\forall (c1: C).(\forall (c2: C).(\forall (t1: T).((cle
64 (CHead c1 k1 t1) c2) \to (\forall (k2: K).(\forall (t2: T).(\forall (i:
65 nat).(flt c1 t1 (CHead c2 k2 t2) (TLRef i)))))))))
67 \lambda (_: K).(\lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda
68 (H: (le (plus (cweight c1) (tweight t1)) (cweight c2))).(\lambda (_:
69 K).(\lambda (t2: T).(\lambda (_: nat).(le_lt_trans (plus (cweight c1)
70 (tweight t1)) (cweight c2) (plus (plus (cweight c2) (tweight t2)) (S O)) H
71 (eq_ind_r nat (plus (S O) (plus (cweight c2) (tweight t2))) (\lambda (n:
72 nat).(lt (cweight c2) n)) (le_lt_n_Sm (cweight c2) (plus (cweight c2)
73 (tweight t2)) (le_plus_l (cweight c2) (tweight t2))) (plus (plus (cweight c2)
74 (tweight t2)) (S O)) (plus_comm (plus (cweight c2) (tweight t2)) (S
78 \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (i: nat).((flt c1
79 t1 c2 (TLRef i)) \to (\forall (k2: K).(\forall (t2: T).(\forall (j: nat).(flt
80 c1 t1 (CHead c2 k2 t2) (TLRef j)))))))))
82 \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (_: nat).(\lambda
83 (H: (lt (plus (cweight c1) (tweight t1)) (plus (cweight c2) (S O)))).(\lambda
84 (_: K).(\lambda (t2: T).(\lambda (_: nat).(lt_le_trans (plus (cweight c1)
85 (tweight t1)) (plus (cweight c2) (S O)) (plus (plus (cweight c2) (tweight
86 t2)) (S O)) H (plus_le_compat (cweight c2) (plus (cweight c2) (tweight t2))
87 (S O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))).
89 theorem flt_wf__q_ind:
90 \forall (P: ((C \to (T \to Prop)))).(((\forall (n: nat).((\lambda (P0: ((C
91 \to (T \to Prop)))).(\lambda (n0: nat).(\forall (c: C).(\forall (t: T).((eq
92 nat (fweight c t) n0) \to (P0 c t)))))) P n))) \to (\forall (c: C).(\forall
95 let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall
96 (c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda
97 (P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (n: nat).(\forall (c:
98 C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t))))))).(\lambda (c:
99 C).(\lambda (t: T).(H (fweight c t) c t (refl_equal nat (fweight c t))))))).
102 \forall (P: ((C \to (T \to Prop)))).(((\forall (c2: C).(\forall (t2:
103 T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1)))))
104 \to (P c2 t2))))) \to (\forall (c: C).(\forall (t: T).(P c t))))
106 let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall
107 (c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda
108 (P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (c2: C).(\forall (t2:
109 T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1)))))
110 \to (P c2 t2)))))).(\lambda (c: C).(\lambda (t: T).(flt_wf__q_ind P (\lambda
111 (n: nat).(lt_wf_ind n (Q P) (\lambda (n0: nat).(\lambda (H0: ((\forall (m:
112 nat).((lt m n0) \to (Q P m))))).(\lambda (c0: C).(\lambda (t0: T).(\lambda
113 (H1: (eq nat (fweight c0 t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1:
114 nat).(\forall (m: nat).((lt m n1) \to (\forall (c1: C).(\forall (t1: T).((eq
115 nat (fweight c1 t1) m) \to (P c1 t1))))))) H0 (fweight c0 t0) H1) in (H c0 t0
116 (\lambda (c1: C).(\lambda (t1: T).(\lambda (H3: (flt c1 t1 c0 t0)).(H2
117 (fweight c1 t1) H3 c1 t1 (refl_equal nat (fweight c1 t1))))))))))))))) c