(* This file was automatically generated: do not edit *********************)
-include "Basic-1/llt/defs.ma".
+include "basic_1/llt/defs.ma".
-include "Basic-1/leq/defs.ma".
+include "basic_1/leq/fwd.ma".
theorem lweight_repl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (eq nat
(lweight a1) (lweight a2)))))
\def
\lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq g a1
-a2)).(leq_ind g (\lambda (a: A).(\lambda (a0: A).(eq nat (lweight a) (lweight
-a0)))) (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1: nat).(\lambda (n2:
-nat).(\lambda (k: nat).(\lambda (_: (eq A (aplus g (ASort h1 n1) k) (aplus g
-(ASort h2 n2) k))).(refl_equal nat O))))))) (\lambda (a0: A).(\lambda (a3:
-A).(\lambda (_: (leq g a0 a3)).(\lambda (H1: (eq nat (lweight a0) (lweight
-a3))).(\lambda (a4: A).(\lambda (a5: A).(\lambda (_: (leq g a4 a5)).(\lambda
-(H3: (eq nat (lweight a4) (lweight a5))).(f_equal nat nat S (plus (lweight
-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 *)
+a2)).(let TMP_3 \def (\lambda (a: A).(\lambda (a0: A).(let TMP_1 \def
+(lweight a) in (let TMP_2 \def (lweight a0) in (eq nat TMP_1 TMP_2))))) in
+(let TMP_4 \def (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1:
+nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda (_: (eq A (aplus g (ASort
+h1 n1) k) (aplus g (ASort h2 n2) k))).(refl_equal nat O))))))) in (let TMP_16
+\def (\lambda (a0: A).(\lambda (a3: A).(\lambda (_: (leq g a0 a3)).(\lambda
+(H1: (eq nat (lweight a0) (lweight a3))).(\lambda (a4: A).(\lambda (a5:
+A).(\lambda (_: (leq g a4 a5)).(\lambda (H3: (eq nat (lweight a4) (lweight
+a5))).(let TMP_5 \def (lweight a0) in (let TMP_6 \def (lweight a4) in (let
+TMP_7 \def (plus TMP_5 TMP_6) in (let TMP_8 \def (lweight a3) in (let TMP_9
+\def (lweight a5) in (let TMP_10 \def (plus TMP_8 TMP_9) in (let TMP_11 \def
+(lweight a0) in (let TMP_12 \def (lweight a3) in (let TMP_13 \def (lweight
+a4) in (let TMP_14 \def (lweight a5) in (let TMP_15 \def (f_equal2 nat nat
+nat plus TMP_11 TMP_12 TMP_13 TMP_14 H1 H3) in (f_equal nat nat S TMP_7
+TMP_10 TMP_15)))))))))))))))))))) in (leq_ind g TMP_3 TMP_4 TMP_16 a1 a2
+H))))))).
theorem llt_repl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).((leq g a1 a2) \to (\forall
(a3: A).((llt a1 a3) \to (llt a2 a3))))))
\def
\lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq g a1
-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 *)
+a2)).(\lambda (a3: A).(\lambda (H0: (lt (lweight a1) (lweight a3))).(let
+TMP_1 \def (lweight a1) in (let TMP_3 \def (\lambda (n: nat).(let TMP_2 \def
+(lweight a3) in (lt n TMP_2))) in (let TMP_4 \def (lweight a2) in (let TMP_5
+\def (lweight_repl g a1 a2 H) in (let H1 \def (eq_ind nat TMP_1 TMP_3 H0
+TMP_4 TMP_5) in H1)))))))))).
theorem llt_trans:
\forall (a1: A).(\forall (a2: A).(\forall (a3: A).((llt a1 a2) \to ((llt a2
a3) \to (llt a1 a3)))))
\def
\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 *)
+a1) (lweight a2))).(\lambda (H0: (lt (lweight a2) (lweight a3))).(let TMP_1
+\def (lweight a1) in (let TMP_2 \def (lweight a2) in (let TMP_3 \def (lweight
+a3) in (lt_trans TMP_1 TMP_2 TMP_3 H H0)))))))).
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 *)
+ \lambda (a1: A).(\lambda (a2: A).(let TMP_1 \def (lweight a1) in (let TMP_2
+\def (lweight a1) in (let TMP_3 \def (lweight a2) in (let TMP_4 \def (plus
+TMP_2 TMP_3) in (let TMP_5 \def (lweight a1) in (let TMP_6 \def (lweight a2)
+in (let TMP_7 \def (le_plus_l TMP_5 TMP_6) in (le_n_S TMP_1 TMP_4
+TMP_7))))))))).
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 (n0: nat).(\forall (a: A).((eq nat (lweight a) n0) \to (P0
-a))))) P n))) \to (\forall (a: A).(P a)))
-\def
- let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a:
-A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((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
-a2) \to (P a1)))) \to (P a2)))) \to (\forall (a: A).(P a)))
-\def
- let Q \def (\lambda (P: ((A \to Prop))).(\lambda (n: nat).(\forall (a:
-A).((eq nat (lweight a) n) \to (P a))))) in (\lambda (P: ((A \to
-Prop))).(\lambda (H: ((\forall (a2: A).(((\forall (a1: A).((lt (lweight a1)
-(lweight a2)) \to (P a1)))) \to (P a2))))).(\lambda (a: A).(llt_wf__q_ind
-(\lambda (a0: A).(P a0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (a0:
-A).(P a0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0)
-\to (Q (\lambda (a0: A).(P a0)) m))))).(\lambda (a0: A).(\lambda (H1: (eq nat
-(lweight a0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall
-(m: nat).((lt m n1) \to (\forall (a1: A).((eq nat (lweight a1) m) \to (P
-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 *)
+ \lambda (a1: A).(\lambda (a2: A).(let TMP_1 \def (lweight a2) in (let TMP_2
+\def (lweight a1) in (let TMP_3 \def (lweight a2) in (let TMP_4 \def (plus
+TMP_2 TMP_3) in (let TMP_5 \def (lweight a1) in (let TMP_6 \def (lweight a2)
+in (let TMP_7 \def (le_plus_r TMP_5 TMP_6) in (le_n_S TMP_1 TMP_4
+TMP_7))))))))).
projects / helm.git / blobdiff