(* This file was automatically generated: do not edit *********************)
-include "Basic-1/sc3/defs.ma".
+include "basic_1/sc3/defs.ma".
-include "Basic-1/sn3/lift1.ma".
+include "basic_1/sn3/lift1.ma".
-include "Basic-1/nf2/lift1.ma".
+include "basic_1/nf2/lift1.ma".
-include "Basic-1/csuba/arity.ma".
+include "basic_1/csuba/arity.ma".
-include "Basic-1/arity/lift1.ma".
+include "basic_1/arity/lift1.ma".
-include "Basic-1/arity/aprem.ma".
+include "basic_1/arity/aprem.ma".
-include "Basic-1/llt/props.ma".
+include "basic_1/llt/props.ma".
-include "Basic-1/drop1/getl.ma".
+include "basic_1/llt/fwd.ma".
-include "Basic-1/drop1/props.ma".
+include "basic_1/drop1/getl.ma".
-include "Basic-1/lift1/props.ma".
+include "basic_1/drop1/props.ma".
-theorem sc3_arity_gen:
+include "basic_1/lift1/drop1.ma".
+
+lemma sc3_arity_gen:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((sc3 g a c
t) \to (arity g c t a)))))
\def
g c t (AHead a0 a1))).(\lambda (_: ((\forall (d: C).(\forall (w: T).((sc3 g
a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat
Appl) w (lift1 is t)))))))))).H3)) H2))))))) a)))).
-(* COMMENTS
-Initial nodes: 369
-END *)
-theorem sc3_repl:
+lemma sc3_repl:
\forall (g: G).(\forall (a1: A).(\forall (c: C).(\forall (t: T).((sc3 g a1 c
t) \to (\forall (a2: A).((leq g a1 a2) \to (sc3 g a2 c t)))))))
\def
Appl) w (lift1 is t)) (H6 d w (H1 x0 (llt_repl g a x0 H8 (AHead a a0)
(llt_head_sx a a0)) d w H12 a (leq_sym g a x0 H8)) is H13) x1 H9))))))) a3
H11))))))) H7))))) H4)))))))))))) a2)) a1)).
-(* COMMENTS
-Initial nodes: 1359
-END *)
-theorem sc3_lift:
+lemma sc3_lift:
\forall (g: G).(\forall (a: A).(\forall (e: C).(\forall (t: T).((sc3 g a e
t) \to (\forall (c: C).(\forall (h: nat).(\forall (d: nat).((drop h d c e)
\to (sc3 g a c (lift h d t))))))))))
(PConsTail is h d) t) (\lambda (t0: T).(sc3 g a1 d0 (THead (Flat Appl) w
t0))) (H_y (drop1_cons_tail c e h d H2 is d0 H7)) (lift1 is (lift h d t))
(lift1_cons_tail t h d is))))))))))) H3))))))))))))) a)).
-(* COMMENTS
-Initial nodes: 849
-END *)
-theorem sc3_lift1:
+lemma sc3_lift1:
\forall (g: G).(\forall (e: C).(\forall (a: A).(\forall (hds:
PList).(\forall (c: C).(\forall (t: T).((sc3 g a e t) \to ((drop1 hds c e)
\to (sc3 g a c (lift1 hds t)))))))))
e)) (sc3 g a c (lift n n0 (lift1 p t))) (\lambda (x: C).(\lambda (H3: (drop n
n0 c x)).(\lambda (H4: (drop1 p x e)).(sc3_lift g a x (lift1 p t) (H x t H0
H4) c n n0 H3)))) H2))))))))))) hds)))).
-(* COMMENTS
-Initial nodes: 289
-END *)
-theorem sc3_abbr:
+lemma sc3_abbr:
\forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (i:
nat).(\forall (d: C).(\forall (v: T).(\forall (c: C).((sc3 g a c (THeads
(Flat Appl) vs (lift (S i) O v))) \to ((getl i c (CHead d (Bind Abbr) v)) \to
H10) (lift1 is (TLRef i)) (lift1_lref is i)) (lift1 is (THeads (Flat Appl) vs
(TLRef i))) (lifts1_flat Appl is (TLRef i) vs)))))) H8)))))))))))
H3))))))))))))) a)).
-(* COMMENTS
-Initial nodes: 1563
-END *)
theorem sc3_cast:
\forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (c: C).(\forall
is t vs))) (lift1 is (THead (Flat Cast) u t)) (lift1_flat Cast is u t))
(lift1 is (THeads (Flat Appl) vs (THead (Flat Cast) u t))) (lifts1_flat Appl
is (THead (Flat Cast) u t) vs))))))))))) H6)))) H3)))))))))))) a)).
-(* COMMENTS
-Initial nodes: 2625
-END *)
-theorem sc3_props__sc3_sn3_abst:
+fact sc3_props__sc3_sn3_abst:
\forall (g: G).(\forall (a: A).(land (\forall (c: C).(\forall (t: T).((sc3 g
a c t) \to (sn3 c t)))) (\forall (vs: TList).(\forall (i: nat).(let t \def
(THeads (Flat Appl) vs (TLRef i)) in (\forall (c: C).((arity g c t a) \to
vs)) (H7 d w H4) (sns3_lifts1 c is d H5 vs H3))) (lift1 is (TLRef i))
(lift1_lref is i)) (lift1 is (THeads (Flat Appl) vs (TLRef i))) (lifts1_flat
Appl is (TLRef i) vs))))) H9)))) H6))))))))))))))))))) a)).
-(* COMMENTS
-Initial nodes: 2737
-END *)
-theorem sc3_sn3:
+lemma sc3_sn3:
\forall (g: G).(\forall (a: A).(\forall (c: C).(\forall (t: T).((sc3 g a c
t) \to (sn3 c t)))))
\def
C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a) \to ((nf2 c0 (TLRef i))
\to ((sns3 c0 vs) \to (sc3 g a c0 (THeads (Flat Appl) vs (TLRef
i))))))))))).(H1 c t H))) H0))))))).
-(* COMMENTS
-Initial nodes: 203
-END *)
-theorem sc3_abst:
+lemma sc3_abst:
\forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (c: C).(\forall
(i: nat).((arity g c (THeads (Flat Appl) vs (TLRef i)) a) \to ((nf2 c (TLRef
i)) \to ((sns3 c vs) \to (sc3 g a c (THeads (Flat Appl) vs (TLRef i))))))))))
nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl) vs0 (TLRef i0)) a) \to
((nf2 c0 (TLRef i0)) \to ((sns3 c0 vs0) \to (sc3 g a c0 (THeads (Flat Appl)
vs0 (TLRef i0))))))))))).(H4 vs i c H H0 H1))) H2)))))))))).
-(* COMMENTS
-Initial nodes: 249
-END *)
theorem sc3_bind:
\forall (g: G).(\forall (b: B).((not (eq B b Abst)) \to (\forall (a1:
d v H3 H8)) (lift1 is (THead (Bind b) v t)) (lift1_bind b is v t)) (lift1 is
(THeads (Flat Appl) vs (THead (Bind b) v t))) (lifts1_flat Appl is (THead
(Bind b) v t) vs))))))))))) H4)))))))))))) a2))))).
-(* COMMENTS
-Initial nodes: 1797
-END *)
theorem sc3_appl:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).(\forall (vs:
v (THead (Bind Abst) w t))) (lift1 is (THeads (Flat Appl) vs (THead (Flat
Appl) v (THead (Bind Abst) w t)))) (lifts1_flat Appl is (THead (Flat Appl) v
(THead (Bind Abst) w t)) vs)))))))))) H4)))))))))))))) a2))).
-(* COMMENTS
-Initial nodes: 1901
-END *)