(* This file was automatically generated: do not edit *********************)
-include "Basic-1/flt/defs.ma".
+include "basic_1/flt/defs.ma".
-include "Basic-1/C/props.ma".
+include "basic_1/C/props.ma".
-theorem flt_thead_sx:
+lemma flt_thead_sx:
\forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c u c
(THead k u t)))))
\def
- \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t:
-T).(le_lt_plus_plus (cweight c) (cweight c) (tweight u) (S (plus (tweight u)
-(tweight t))) (le_n (cweight c)) (le_n_S (tweight u) (plus (tweight u)
-(tweight t)) (le_plus_l (tweight u) (tweight t))))))).
-(* COMMENTS
-Initial nodes: 65
-END *)
+ \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(lt_reg_l
+(tweight u) (S (plus (tweight u) (tweight t))) (cweight c) (le_n_S (tweight
+u) (plus (tweight u) (tweight t)) (le_plus_l (tweight u) (tweight t))))))).
-theorem flt_thead_dx:
+lemma flt_thead_dx:
\forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c t c
(THead k u t)))))
\def
- \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t:
-T).(le_lt_plus_plus (cweight c) (cweight c) (tweight t) (S (plus (tweight u)
-(tweight t))) (le_n (cweight c)) (le_n_S (tweight t) (plus (tweight u)
-(tweight t)) (le_plus_r (tweight u) (tweight t))))))).
-(* COMMENTS
-Initial nodes: 65
-END *)
+ \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(lt_reg_l
+(tweight t) (S (plus (tweight u) (tweight t))) (cweight c) (le_n_S (tweight
+t) (plus (tweight u) (tweight t)) (le_plus_r (tweight u) (tweight t))))))).
-theorem flt_shift:
+lemma flt_shift:
\forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt (CHead c
k u) t c (THead k u t)))))
\def
t))) (plus_assoc_l (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S
(plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u)
(tweight t))))))).
-(* COMMENTS
-Initial nodes: 179
-END *)
-theorem flt_arith0:
+lemma flt_arith0:
\forall (k: K).(\forall (c: C).(\forall (t: T).(\forall (i: nat).(flt c t
(CHead c k t) (TLRef i)))))
\def
\lambda (_: K).(\lambda (c: C).(\lambda (t: T).(\lambda (_:
nat).(lt_x_plus_x_Sy (plus (cweight c) (tweight t)) O)))).
-(* COMMENTS
-Initial nodes: 21
-END *)
-theorem flt_arith1:
+lemma flt_arith1:
\forall (k1: K).(\forall (c1: C).(\forall (c2: C).(\forall (t1: T).((cle
(CHead c1 k1 t1) c2) \to (\forall (k2: K).(\forall (t2: T).(\forall (i:
nat).(flt c1 t1 (CHead c2 k2 t2) (TLRef i)))))))))
(tweight t2)) (le_plus_l (cweight c2) (tweight t2))) (plus (plus (cweight c2)
(tweight t2)) (S O)) (plus_sym (plus (cweight c2) (tweight t2)) (S
O))))))))))).
-(* COMMENTS
-Initial nodes: 151
-END *)
-theorem flt_arith2:
+lemma flt_arith2:
\forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (i: nat).((flt c1
t1 c2 (TLRef i)) \to (\forall (k2: K).(\forall (t2: T).(\forall (j: nat).(flt
c1 t1 (CHead c2 k2 t2) (TLRef j)))))))))
(tweight t1)) (plus (cweight c2) (S O)) (plus (plus (cweight c2) (tweight
t2)) (S O)) H (le_plus_plus (cweight c2) (plus (cweight c2) (tweight t2)) (S
O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))).
-(* COMMENTS
-Initial nodes: 115
-END *)
+
+lemma cle_flt_trans:
+ \forall (c1: C).(\forall (c2: C).((cle c1 c2) \to (\forall (c3: C).(\forall
+(u2: T).(\forall (u3: T).((flt c2 u2 c3 u3) \to (flt c1 u2 c3 u3)))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (le (cweight c1) (cweight
+c2))).(\lambda (c3: C).(\lambda (u2: T).(\lambda (u3: T).(\lambda (H0: (lt
+(plus (cweight c2) (tweight u2)) (plus (cweight c3) (tweight
+u3)))).(le_lt_trans (plus (cweight c1) (tweight u2)) (plus (cweight c2)
+(tweight u2)) (plus (cweight c3) (tweight u3)) (le_plus_plus (cweight c1)
+(cweight c2) (tweight u2) (tweight u2) H (le_n (tweight u2))) H0))))))).
theorem flt_trans:
\forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).((flt c1
(H: (lt (fweight c1 t1) (fweight c2 t2))).(\lambda (c3: C).(\lambda (t3:
T).(\lambda (H0: (lt (fweight c2 t2) (fweight c3 t3))).(lt_trans (fweight c1
t1) (fweight c2 t2) (fweight c3 t3) H H0)))))))).
-(* COMMENTS
-Initial nodes: 63
-END *)
-
-theorem flt_wf__q_ind:
- \forall (P: ((C \to (T \to Prop)))).(((\forall (n: nat).((\lambda (P0: ((C
-\to (T \to Prop)))).(\lambda (n0: nat).(\forall (c: C).(\forall (t: T).((eq
-nat (fweight c t) n0) \to (P0 c t)))))) P n))) \to (\forall (c: C).(\forall
-(t: T).(P c t))))
-\def
- let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall
-(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda
-(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (n: nat).(\forall (c:
-C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t))))))).(\lambda (c:
-C).(\lambda (t: T).(H (fweight c t) c t (refl_equal nat (fweight c t))))))).
-(* COMMENTS
-Initial nodes: 85
-END *)
-
-theorem flt_wf_ind:
- \forall (P: ((C \to (T \to Prop)))).(((\forall (c2: C).(\forall (t2:
-T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1)))))
-\to (P c2 t2))))) \to (\forall (c: C).(\forall (t: T).(P c t))))
-\def
- let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall
-(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda
-(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (c2: C).(\forall (t2:
-T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1)))))
-\to (P c2 t2)))))).(\lambda (c: C).(\lambda (t: T).(flt_wf__q_ind P (\lambda
-(n: nat).(lt_wf_ind n (Q P) (\lambda (n0: nat).(\lambda (H0: ((\forall (m:
-nat).((lt m n0) \to (Q P m))))).(\lambda (c0: C).(\lambda (t0: T).(\lambda
-(H1: (eq nat (fweight c0 t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1:
-nat).(\forall (m: nat).((lt m n1) \to (\forall (c1: C).(\forall (t1: T).((eq
-nat (fweight c1 t1) m) \to (P c1 t1))))))) H0 (fweight c0 t0) H1) in (H c0 t0
-(\lambda (c1: C).(\lambda (t1: T).(\lambda (H3: (flt c1 t1 c0 t0)).(H2
-(fweight c1 t1) H3 c1 t1 (refl_equal nat (fweight c1 t1))))))))))))))) c
-t))))).
-(* COMMENTS
-Initial nodes: 211
-END *)
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