include "basic_1/tlt/defs.ma".
-theorem tlt_wf__q_ind:
+fact tlt_wf__q_ind:
\forall (P: ((T \to Prop))).(((\forall (n: nat).((\lambda (P0: ((T \to
Prop))).(\lambda (n0: nat).(\forall (t: T).((eq nat (weight t) n0) \to (P0
t))))) P n))) \to (\forall (t: T).(P t)))
let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t:
T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to
Prop))).(\lambda (H: ((\forall (n: nat).(\forall (t: T).((eq nat (weight t)
-n) \to (P t)))))).(\lambda (t: T).(let TMP_1 \def (weight t) in (let TMP_2
-\def (weight t) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 t
-TMP_3))))))).
+n) \to (P t)))))).(\lambda (t: T).(H (weight t) t (refl_equal nat (weight
+t)))))).
-theorem tlt_wf_ind:
+lemma tlt_wf_ind:
\forall (P: ((T \to Prop))).(((\forall (t: T).(((\forall (v: T).((tlt v t)
\to (P v)))) \to (P t)))) \to (\forall (t: T).(P t)))
\def
let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t:
T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to
Prop))).(\lambda (H: ((\forall (t: T).(((\forall (v: T).((lt (weight v)
-(weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(let TMP_1 \def
-(\lambda (t0: T).(P t0)) in (let TMP_11 \def (\lambda (n: nat).(let TMP_2
-\def (\lambda (t0: T).(P t0)) in (let TMP_3 \def (Q TMP_2) in (let TMP_10
-\def (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) \to (Q
-(\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat
-(weight t0) n0)).(let TMP_4 \def (\lambda (n1: nat).(\forall (m: nat).((lt m
-n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P t1)))))) in (let
-TMP_5 \def (weight t0) in (let H2 \def (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) in
-(let TMP_9 \def (\lambda (v: T).(\lambda (H3: (lt (weight v) (weight
-t0))).(let TMP_6 \def (weight v) in (let TMP_7 \def (weight v) in (let TMP_8
-\def (refl_equal nat TMP_7) in (H2 TMP_6 H3 v TMP_8)))))) in (H t0
-TMP_9))))))))) in (lt_wf_ind n TMP_3 TMP_10))))) in (tlt_wf__q_ind TMP_1
-TMP_11 t)))))).
+(weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(tlt_wf__q_ind
+(\lambda (t0: T).(P t0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (t0:
+T).(P t0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0)
+\to (Q (\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat
+(weight t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall
+(m: nat).((lt m n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P
+t1)))))) H0 (weight t0) H1) in (H t0 (\lambda (v: T).(\lambda (H3: (lt
+(weight v) (weight t0))).(H2 (weight v) H3 v (refl_equal nat (weight
+v))))))))))))) t)))).