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
(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
(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
(plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u)
(tweight t))))))).
-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)))).
-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)) (S O)) (plus_sym (plus (cweight c2) (tweight t2)) (S
O))))))))))).
-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)))))))))
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))))))))))).
-theorem cle_flt_trans:
+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