(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/llt/defs.ma".
+include "Basic-1/llt/defs.ma".
-include "LambdaDelta-1/leq/defs.ma".
+include "Basic-1/leq/defs.ma".
theorem lweight_repl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (eq nat
a0) (lweight a4)) (plus (lweight a3) (lweight a5)) (f_equal2 nat nat nat plus
(lweight a0) (lweight a3) (lweight a4) (lweight a5) H1 H3)))))))))) a1 a2
H)))).
+(* COMMENTS
+Initial nodes: 189
+END *)
theorem llt_repl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (\forall
a2)).(\lambda (a3: A).(\lambda (H0: (lt (lweight a1) (lweight a3))).(let H1
\def (eq_ind nat (lweight a1) (\lambda (n: nat).(lt n (lweight a3))) H0
(lweight a2) (lweight_repl g a1 a2 H)) in H1)))))).
+(* COMMENTS
+Initial nodes: 61
+END *)
theorem llt_trans:
\forall (a1: A).(\forall (a2: A).(\forall (a3: A).((llt a1 a2) \to ((llt a2
\lambda (a1: A).(\lambda (a2: A).(\lambda (a3: A).(\lambda (H: (lt (lweight
a1) (lweight a2))).(\lambda (H0: (lt (lweight a2) (lweight a3))).(lt_trans
(lweight a1) (lweight a2) (lweight a3) H H0))))).
+(* COMMENTS
+Initial nodes: 43
+END *)
theorem llt_head_sx:
\forall (a1: A).(\forall (a2: A).(llt a1 (AHead a1 a2)))
\def
\lambda (a1: A).(\lambda (a2: A).(le_n_S (lweight a1) (plus (lweight a1)
(lweight a2)) (le_plus_l (lweight a1) (lweight a2)))).
+(* COMMENTS
+Initial nodes: 29
+END *)
theorem llt_head_dx:
\forall (a1: A).(\forall (a2: A).(llt a2 (AHead a1 a2)))
\def
\lambda (a1: A).(\lambda (a2: A).(le_n_S (lweight a2) (plus (lweight a1)
(lweight a2)) (le_plus_r (lweight a1) (lweight a2)))).
+(* COMMENTS
+Initial nodes: 29
+END *)
theorem llt_wf__q_ind:
\forall (P: ((A \to Prop))).(((\forall (n: nat).((\lambda (P0: ((A \to
Prop))).(\lambda (H: ((\forall (n: nat).(\forall (a: A).((eq nat (lweight a)
n) \to (P a)))))).(\lambda (a: A).(H (lweight a) a (refl_equal nat (lweight
a)))))).
+(* COMMENTS
+Initial nodes: 61
+END *)
theorem llt_wf_ind:
\forall (P: ((A \to Prop))).(((\forall (a2: A).(((\forall (a1: A).((llt a1
a1)))))) H0 (lweight a0) H1) in (H a0 (\lambda (a1: A).(\lambda (H3: (lt
(lweight a1) (lweight a0))).(H2 (lweight a1) H3 a1 (refl_equal nat (lweight
a1))))))))))))) a)))).
+(* COMMENTS
+Initial nodes: 179
+END *)