From d795687ffe924872a5e36122c2bd3069d6409454 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Sun, 8 Feb 2015 17:13:27 +0000 Subject: [PATCH] components: clear getl cimp if anticipated, getl/drop.ma causes "Out of mamory" in matitac --- .../contribs/lambdadelta/basic_1/cimp/defs.ma | 7 +- .../lambdadelta/basic_1/cimp/props.ma | 227 +++++++---- .../lambdadelta/basic_1/clear/defs.ma | 2 +- .../lambdadelta/basic_1/clear/drop.ma | 372 +++++++++++------- .../contribs/lambdadelta/basic_1/clear/fwd.ma | 342 ++++++++++------ .../lambdadelta/basic_1/clear/props.ma | 224 +++++------ .../lambdadelta/basic_1/getl/clear.ma | 262 ++++++------ .../contribs/lambdadelta/basic_1/getl/dec.ma | 208 ++++++---- .../contribs/lambdadelta/basic_1/getl/defs.ma | 4 +- .../contribs/lambdadelta/basic_1/getl/drop.ma | 271 ++++++------- .../contribs/lambdadelta/basic_1/getl/flt.ma | 108 +++-- .../contribs/lambdadelta/basic_1/getl/fwd.ma | 230 +++++++---- .../contribs/lambdadelta/basic_1/getl/getl.ma | 47 +-- .../lambdadelta/basic_1/getl/props.ma | 109 +++-- 14 files changed, 1409 insertions(+), 1004 deletions(-) diff --git a/matita/matita/contribs/lambdadelta/basic_1/cimp/defs.ma b/matita/matita/contribs/lambdadelta/basic_1/cimp/defs.ma index b45b64b59..fce9abdd1 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/cimp/defs.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/cimp/defs.ma @@ -14,12 +14,13 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/defs.ma". +include "basic_1/getl/defs.ma". definition cimp: C \to (C \to Prop) \def \lambda (c1: C).(\lambda (c2: C).(\forall (b: B).(\forall (d1: C).(\forall -(w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to (ex C -(\lambda (d2: C).(getl h c2 (CHead d2 (Bind b) w)))))))))). +(w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to (let TMP_3 +\def (\lambda (d2: C).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead d2 +TMP_1 w) in (getl h c2 TMP_2)))) in (ex C TMP_3)))))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/cimp/props.ma b/matita/matita/contribs/lambdadelta/basic_1/cimp/props.ma index 0834a7afe..92af7b3c8 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/cimp/props.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/cimp/props.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/cimp/defs.ma". +include "basic_1/cimp/defs.ma". -include "Basic-1/getl/getl.ma". +include "basic_1/getl/getl.ma". theorem cimp_flat_sx: \forall (f: F).(\forall (c: C).(\forall (v: T).(cimp (CHead c (Flat f) v) @@ -24,20 +24,28 @@ c))) \def \lambda (f: F).(\lambda (c: C).(\lambda (v: T).(\lambda (b: B).(\lambda (d1: C).(\lambda (w: T).(\lambda (h: nat).(\lambda (H: (getl h (CHead c (Flat f) -v) (CHead d1 (Bind b) w))).(nat_ind (\lambda (n: nat).((getl n (CHead c (Flat -f) v) (CHead d1 (Bind b) w)) \to (ex C (\lambda (d2: C).(getl n c (CHead d2 -(Bind b) w)))))) (\lambda (H0: (getl O (CHead c (Flat f) v) (CHead d1 (Bind -b) w))).(ex_intro C (\lambda (d2: C).(getl O c (CHead d2 (Bind b) w))) d1 -(getl_intro O c (CHead d1 (Bind b) w) c (drop_refl c) (clear_gen_flat f c -(CHead d1 (Bind b) w) v (getl_gen_O (CHead c (Flat f) v) (CHead d1 (Bind b) -w) H0))))) (\lambda (h0: nat).(\lambda (_: (((getl h0 (CHead c (Flat f) v) +v) (CHead d1 (Bind b) w))).(let TMP_4 \def (\lambda (n: nat).((getl n (CHead +c (Flat f) v) (CHead d1 (Bind b) w)) \to (let TMP_3 \def (\lambda (d2: +C).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead d2 TMP_1 w) in (getl n +c TMP_2)))) in (ex C TMP_3)))) in (let TMP_20 \def (\lambda (H0: (getl O +(CHead c (Flat f) v) (CHead d1 (Bind b) w))).(let TMP_7 \def (\lambda (d2: +C).(let TMP_5 \def (Bind b) in (let TMP_6 \def (CHead d2 TMP_5 w) in (getl O +c TMP_6)))) in (let TMP_8 \def (Bind b) in (let TMP_9 \def (CHead d1 TMP_8 w) +in (let TMP_10 \def (drop_refl c) in (let TMP_11 \def (Bind b) in (let TMP_12 +\def (CHead d1 TMP_11 w) in (let TMP_13 \def (Flat f) in (let TMP_14 \def +(CHead c TMP_13 v) in (let TMP_15 \def (Bind b) in (let TMP_16 \def (CHead d1 +TMP_15 w) in (let TMP_17 \def (getl_gen_O TMP_14 TMP_16 H0) in (let TMP_18 +\def (clear_gen_flat f c TMP_12 v TMP_17) in (let TMP_19 \def (getl_intro O c +TMP_9 c TMP_10 TMP_18) in (ex_intro C TMP_7 d1 TMP_19))))))))))))))) in (let +TMP_29 \def (\lambda (h0: nat).(\lambda (_: (((getl h0 (CHead c (Flat f) v) (CHead d1 (Bind b) w)) \to (ex C (\lambda (d2: C).(getl h0 c (CHead d2 (Bind b) w))))))).(\lambda (H0: (getl (S h0) (CHead c (Flat f) v) (CHead d1 (Bind -b) w))).(ex_intro C (\lambda (d2: C).(getl (S h0) c (CHead d2 (Bind b) w))) -d1 (getl_gen_S (Flat f) c (CHead d1 (Bind b) w) v h0 H0))))) h H)))))))). -(* COMMENTS -Initial nodes: 327 -END *) +b) w))).(let TMP_24 \def (\lambda (d2: C).(let TMP_21 \def (S h0) in (let +TMP_22 \def (Bind b) in (let TMP_23 \def (CHead d2 TMP_22 w) in (getl TMP_21 +c TMP_23))))) in (let TMP_25 \def (Flat f) in (let TMP_26 \def (Bind b) in +(let TMP_27 \def (CHead d1 TMP_26 w) in (let TMP_28 \def (getl_gen_S TMP_25 c +TMP_27 v h0 H0) in (ex_intro C TMP_24 d1 TMP_28))))))))) in (nat_ind TMP_4 +TMP_20 TMP_29 h H))))))))))). theorem cimp_flat_dx: \forall (f: F).(\forall (c: C).(\forall (v: T).(cimp c (CHead c (Flat f) @@ -45,11 +53,11 @@ v)))) \def \lambda (f: F).(\lambda (c: C).(\lambda (v: T).(\lambda (b: B).(\lambda (d1: C).(\lambda (w: T).(\lambda (h: nat).(\lambda (H: (getl h c (CHead d1 (Bind -b) w))).(ex_intro C (\lambda (d2: C).(getl h (CHead c (Flat f) v) (CHead d2 -(Bind b) w))) d1 (getl_flat c (CHead d1 (Bind b) w) h H f v))))))))). -(* COMMENTS -Initial nodes: 83 -END *) +b) w))).(let TMP_5 \def (\lambda (d2: C).(let TMP_1 \def (Flat f) in (let +TMP_2 \def (CHead c TMP_1 v) in (let TMP_3 \def (Bind b) in (let TMP_4 \def +(CHead d2 TMP_3 w) in (getl h TMP_2 TMP_4)))))) in (let TMP_6 \def (Bind b) +in (let TMP_7 \def (CHead d1 TMP_6 w) in (let TMP_8 \def (getl_flat c TMP_7 h +H f v) in (ex_intro C TMP_5 d1 TMP_8)))))))))))). theorem cimp_bind: \forall (c1: C).(\forall (c2: C).((cimp c1 c2) \to (\forall (b: B).(\forall @@ -60,42 +68,72 @@ C).(\forall (w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to (ex C (\lambda (d2: C).(getl h c2 (CHead d2 (Bind b) w))))))))))).(\lambda (b: B).(\lambda (v: T).(\lambda (b0: B).(\lambda (d1: C).(\lambda (w: T).(\lambda (h: nat).(\lambda (H0: (getl h (CHead c1 (Bind b) v) (CHead d1 -(Bind b0) w))).(nat_ind (\lambda (n: nat).((getl n (CHead c1 (Bind b) v) -(CHead d1 (Bind b0) w)) \to (ex C (\lambda (d2: C).(getl n (CHead c2 (Bind b) -v) (CHead d2 (Bind b0) w)))))) (\lambda (H1: (getl O (CHead c1 (Bind b) v) -(CHead d1 (Bind b0) w))).(let H2 \def (f_equal C C (\lambda (e: C).(match e -in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) -\Rightarrow c])) (CHead d1 (Bind b0) w) (CHead c1 (Bind b) v) (clear_gen_bind -b c1 (CHead d1 (Bind b0) w) v (getl_gen_O (CHead c1 (Bind b) v) (CHead d1 -(Bind b0) w) H1))) in ((let H3 \def (f_equal C B (\lambda (e: C).(match e in -C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b0 | (CHead _ k _) -\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b1) -\Rightarrow b1 | (Flat _) \Rightarrow b0])])) (CHead d1 (Bind b0) w) (CHead -c1 (Bind b) v) (clear_gen_bind b c1 (CHead d1 (Bind b0) w) v (getl_gen_O -(CHead c1 (Bind b) v) (CHead d1 (Bind b0) w) H1))) in ((let H4 \def (f_equal -C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) -\Rightarrow w | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b0) w) (CHead -c1 (Bind b) v) (clear_gen_bind b c1 (CHead d1 (Bind b0) w) v (getl_gen_O -(CHead c1 (Bind b) v) (CHead d1 (Bind b0) w) H1))) in (\lambda (H5: (eq B b0 -b)).(\lambda (_: (eq C d1 c1)).(eq_ind_r T v (\lambda (t: T).(ex C (\lambda -(d2: C).(getl O (CHead c2 (Bind b) v) (CHead d2 (Bind b0) t))))) (eq_ind_r B -b (\lambda (b1: B).(ex C (\lambda (d2: C).(getl O (CHead c2 (Bind b) v) -(CHead d2 (Bind b1) v))))) (ex_intro C (\lambda (d2: C).(getl O (CHead c2 -(Bind b) v) (CHead d2 (Bind b) v))) c2 (getl_refl b c2 v)) b0 H5) w H4)))) -H3)) H2))) (\lambda (h0: nat).(\lambda (_: (((getl h0 (CHead c1 (Bind b) v) -(CHead d1 (Bind b0) w)) \to (ex C (\lambda (d2: C).(getl h0 (CHead c2 (Bind -b) v) (CHead d2 (Bind b0) w))))))).(\lambda (H1: (getl (S h0) (CHead c1 (Bind -b) v) (CHead d1 (Bind b0) w))).(let H_x \def (H b0 d1 w (r (Bind b) h0) -(getl_gen_S (Bind b) c1 (CHead d1 (Bind b0) w) v h0 H1)) in (let H2 \def H_x -in (ex_ind C (\lambda (d2: C).(getl h0 c2 (CHead d2 (Bind b0) w))) (ex C -(\lambda (d2: C).(getl (S h0) (CHead c2 (Bind b) v) (CHead d2 (Bind b0) w)))) -(\lambda (x: C).(\lambda (H3: (getl h0 c2 (CHead x (Bind b0) w))).(ex_intro C -(\lambda (d2: C).(getl (S h0) (CHead c2 (Bind b) v) (CHead d2 (Bind b0) w))) -x (getl_head (Bind b) h0 c2 (CHead x (Bind b0) w) H3 v)))) H2)))))) h -H0)))))))))). -(* COMMENTS -Initial nodes: 817 -END *) +(Bind b0) w))).(let TMP_6 \def (\lambda (n: nat).((getl n (CHead c1 (Bind b) +v) (CHead d1 (Bind b0) w)) \to (let TMP_5 \def (\lambda (d2: C).(let TMP_1 +\def (Bind b) in (let TMP_2 \def (CHead c2 TMP_1 v) in (let TMP_3 \def (Bind +b0) in (let TMP_4 \def (CHead d2 TMP_3 w) in (getl n TMP_2 TMP_4)))))) in (ex +C TMP_5)))) in (let TMP_68 \def (\lambda (H1: (getl O (CHead c1 (Bind b) v) +(CHead d1 (Bind b0) w))).(let TMP_7 \def (\lambda (e: C).(match e with +[(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c])) in (let TMP_8 \def +(Bind b0) in (let TMP_9 \def (CHead d1 TMP_8 w) in (let TMP_10 \def (Bind b) +in (let TMP_11 \def (CHead c1 TMP_10 v) in (let TMP_12 \def (Bind b0) in (let +TMP_13 \def (CHead d1 TMP_12 w) in (let TMP_14 \def (Bind b) in (let TMP_15 +\def (CHead c1 TMP_14 v) in (let TMP_16 \def (Bind b0) in (let TMP_17 \def +(CHead d1 TMP_16 w) in (let TMP_18 \def (getl_gen_O TMP_15 TMP_17 H1) in (let +TMP_19 \def (clear_gen_bind b c1 TMP_13 v TMP_18) in (let H2 \def (f_equal C +C TMP_7 TMP_9 TMP_11 TMP_19) in (let TMP_20 \def (\lambda (e: C).(match e +with [(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow (match k with +[(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b0])])) in (let TMP_21 \def +(Bind b0) in (let TMP_22 \def (CHead d1 TMP_21 w) in (let TMP_23 \def (Bind +b) in (let TMP_24 \def (CHead c1 TMP_23 v) in (let TMP_25 \def (Bind b0) in +(let TMP_26 \def (CHead d1 TMP_25 w) in (let TMP_27 \def (Bind b) in (let +TMP_28 \def (CHead c1 TMP_27 v) in (let TMP_29 \def (Bind b0) in (let TMP_30 +\def (CHead d1 TMP_29 w) in (let TMP_31 \def (getl_gen_O TMP_28 TMP_30 H1) in +(let TMP_32 \def (clear_gen_bind b c1 TMP_26 v TMP_31) in (let H3 \def +(f_equal C B TMP_20 TMP_22 TMP_24 TMP_32) in (let TMP_33 \def (\lambda (e: +C).(match e with [(CSort _) \Rightarrow w | (CHead _ _ t) \Rightarrow t])) in +(let TMP_34 \def (Bind b0) in (let TMP_35 \def (CHead d1 TMP_34 w) in (let +TMP_36 \def (Bind b) in (let TMP_37 \def (CHead c1 TMP_36 v) in (let TMP_38 +\def (Bind b0) in (let TMP_39 \def (CHead d1 TMP_38 w) in (let TMP_40 \def +(Bind b) in (let TMP_41 \def (CHead c1 TMP_40 v) in (let TMP_42 \def (Bind +b0) in (let TMP_43 \def (CHead d1 TMP_42 w) in (let TMP_44 \def (getl_gen_O +TMP_41 TMP_43 H1) in (let TMP_45 \def (clear_gen_bind b c1 TMP_39 v TMP_44) +in (let H4 \def (f_equal C T TMP_33 TMP_35 TMP_37 TMP_45) in (let TMP_66 \def +(\lambda (H5: (eq B b0 b)).(\lambda (_: (eq C d1 c1)).(let TMP_51 \def +(\lambda (t: T).(let TMP_50 \def (\lambda (d2: C).(let TMP_46 \def (Bind b) +in (let TMP_47 \def (CHead c2 TMP_46 v) in (let TMP_48 \def (Bind b0) in (let +TMP_49 \def (CHead d2 TMP_48 t) in (getl O TMP_47 TMP_49)))))) in (ex C +TMP_50))) in (let TMP_57 \def (\lambda (b1: B).(let TMP_56 \def (\lambda (d2: +C).(let TMP_52 \def (Bind b) in (let TMP_53 \def (CHead c2 TMP_52 v) in (let +TMP_54 \def (Bind b1) in (let TMP_55 \def (CHead d2 TMP_54 v) in (getl O +TMP_53 TMP_55)))))) in (ex C TMP_56))) in (let TMP_62 \def (\lambda (d2: +C).(let TMP_58 \def (Bind b) in (let TMP_59 \def (CHead c2 TMP_58 v) in (let +TMP_60 \def (Bind b) in (let TMP_61 \def (CHead d2 TMP_60 v) in (getl O +TMP_59 TMP_61)))))) in (let TMP_63 \def (getl_refl b c2 v) in (let TMP_64 +\def (ex_intro C TMP_62 c2 TMP_63) in (let TMP_65 \def (eq_ind_r B b TMP_57 +TMP_64 b0 H5) in (eq_ind_r T v TMP_51 TMP_65 w H4))))))))) in (let TMP_67 +\def (TMP_66 H3) in (TMP_67 H2)))))))))))))))))))))))))))))))))))))))))))))) +in (let TMP_96 \def (\lambda (h0: nat).(\lambda (_: (((getl h0 (CHead c1 +(Bind b) v) (CHead d1 (Bind b0) w)) \to (ex C (\lambda (d2: C).(getl h0 +(CHead c2 (Bind b) v) (CHead d2 (Bind b0) w))))))).(\lambda (H1: (getl (S h0) +(CHead c1 (Bind b) v) (CHead d1 (Bind b0) w))).(let TMP_69 \def (Bind b) in +(let TMP_70 \def (r TMP_69 h0) in (let TMP_71 \def (Bind b) in (let TMP_72 +\def (Bind b0) in (let TMP_73 \def (CHead d1 TMP_72 w) in (let TMP_74 \def +(getl_gen_S TMP_71 c1 TMP_73 v h0 H1) in (let H_x \def (H b0 d1 w TMP_70 +TMP_74) in (let H2 \def H_x in (let TMP_77 \def (\lambda (d2: C).(let TMP_75 +\def (Bind b0) in (let TMP_76 \def (CHead d2 TMP_75 w) in (getl h0 c2 +TMP_76)))) in (let TMP_83 \def (\lambda (d2: C).(let TMP_78 \def (S h0) in +(let TMP_79 \def (Bind b) in (let TMP_80 \def (CHead c2 TMP_79 v) in (let +TMP_81 \def (Bind b0) in (let TMP_82 \def (CHead d2 TMP_81 w) in (getl TMP_78 +TMP_80 TMP_82))))))) in (let TMP_84 \def (ex C TMP_83) in (let TMP_95 \def +(\lambda (x: C).(\lambda (H3: (getl h0 c2 (CHead x (Bind b0) w))).(let TMP_90 +\def (\lambda (d2: C).(let TMP_85 \def (S h0) in (let TMP_86 \def (Bind b) in +(let TMP_87 \def (CHead c2 TMP_86 v) in (let TMP_88 \def (Bind b0) in (let +TMP_89 \def (CHead d2 TMP_88 w) in (getl TMP_85 TMP_87 TMP_89))))))) in (let +TMP_91 \def (Bind b) in (let TMP_92 \def (Bind b0) in (let TMP_93 \def (CHead +x TMP_92 w) in (let TMP_94 \def (getl_head TMP_91 h0 c2 TMP_93 H3 v) in +(ex_intro C TMP_90 x TMP_94)))))))) in (ex_ind C TMP_77 TMP_84 TMP_95 +H2)))))))))))))))) in (nat_ind TMP_6 TMP_68 TMP_96 h H0))))))))))))). theorem cimp_getl_conf: \forall (c1: C).(\forall (c2: C).((cimp c1 c2) \to (\forall (b: B).(\forall @@ -108,32 +146,59 @@ C).(\forall (w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to (ex C (\lambda (d2: C).(getl h c2 (CHead d2 (Bind b) w))))))))))).(\lambda (b: B).(\lambda (d1: C).(\lambda (w: T).(\lambda (i: nat).(\lambda (H0: (getl i c1 (CHead d1 (Bind b) w))).(let H_x \def (H b d1 w i H0) in (let H1 \def -H_x in (ex_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind b) w))) (ex2 C +H_x in (let TMP_3 \def (\lambda (d2: C).(let TMP_1 \def (Bind b) in (let +TMP_2 \def (CHead d2 TMP_1 w) in (getl i c2 TMP_2)))) in (let TMP_7 \def (\lambda (d2: C).(\forall (b0: B).(\forall (d3: C).(\forall (w0: T).(\forall -(h: nat).((getl h d1 (CHead d3 (Bind b0) w0)) \to (ex C (\lambda (d4: -C).(getl h d2 (CHead d4 (Bind b0) w0)))))))))) (\lambda (d2: C).(getl i c2 -(CHead d2 (Bind b) w)))) (\lambda (x: C).(\lambda (H2: (getl i c2 (CHead x -(Bind b) w))).(ex_intro2 C (\lambda (d2: C).(\forall (b0: B).(\forall (d3: -C).(\forall (w0: T).(\forall (h: nat).((getl h d1 (CHead d3 (Bind b0) w0)) -\to (ex C (\lambda (d4: C).(getl h d2 (CHead d4 (Bind b0) w0)))))))))) -(\lambda (d2: C).(getl i c2 (CHead d2 (Bind b) w))) x (\lambda (b0: +(h: nat).((getl h d1 (CHead d3 (Bind b0) w0)) \to (let TMP_6 \def (\lambda +(d4: C).(let TMP_4 \def (Bind b0) in (let TMP_5 \def (CHead d4 TMP_4 w0) in +(getl h d2 TMP_5)))) in (ex C TMP_6)))))))) in (let TMP_10 \def (\lambda (d2: +C).(let TMP_8 \def (Bind b) in (let TMP_9 \def (CHead d2 TMP_8 w) in (getl i +c2 TMP_9)))) in (let TMP_11 \def (ex2 C TMP_7 TMP_10) in (let TMP_82 \def +(\lambda (x: C).(\lambda (H2: (getl i c2 (CHead x (Bind b) w))).(let TMP_15 +\def (\lambda (d2: C).(\forall (b0: B).(\forall (d3: C).(\forall (w0: +T).(\forall (h: nat).((getl h d1 (CHead d3 (Bind b0) w0)) \to (let TMP_14 +\def (\lambda (d4: C).(let TMP_12 \def (Bind b0) in (let TMP_13 \def (CHead +d4 TMP_12 w0) in (getl h d2 TMP_13)))) in (ex C TMP_14)))))))) in (let TMP_18 +\def (\lambda (d2: C).(let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead d2 +TMP_16 w) in (getl i c2 TMP_17)))) in (let TMP_81 \def (\lambda (b0: B).(\lambda (d0: C).(\lambda (w0: T).(\lambda (h: nat).(\lambda (H3: (getl h -d1 (CHead d0 (Bind b0) w0))).(let H_y \def (getl_trans (S h) c1 (CHead d1 -(Bind b) w) i H0) in (let H_x0 \def (H b0 d0 w0 (plus (S h) i) (H_y (CHead d0 -(Bind b0) w0) (getl_head (Bind b) h d1 (CHead d0 (Bind b0) w0) H3 w))) in -(let H4 \def H_x0 in (ex_ind C (\lambda (d2: C).(getl (S (plus h i)) c2 -(CHead d2 (Bind b0) w0))) (ex C (\lambda (d2: C).(getl h x (CHead d2 (Bind -b0) w0)))) (\lambda (x0: C).(\lambda (H5: (getl (S (plus h i)) c2 (CHead x0 -(Bind b0) w0))).(let H_y0 \def (getl_conf_le (S (plus h i)) (CHead x0 (Bind -b0) w0) c2 H5 (CHead x (Bind b) w) i H2) in (let H6 \def (refl_equal nat -(plus (S h) i)) in (let H7 \def (eq_ind nat (S (plus h i)) (\lambda (n: -nat).(getl (minus n i) (CHead x (Bind b) w) (CHead x0 (Bind b0) w0))) (H_y0 -(le_S i (plus h i) (le_plus_r h i))) (plus (S h) i) H6) in (let H8 \def -(eq_ind nat (minus (plus (S h) i) i) (\lambda (n: nat).(getl n (CHead x (Bind -b) w) (CHead x0 (Bind b0) w0))) H7 (S h) (minus_plus_r (S h) i)) in (ex_intro -C (\lambda (d2: C).(getl h x (CHead d2 (Bind b0) w0))) x0 (getl_gen_S (Bind -b) x (CHead x0 (Bind b0) w0) w h H8)))))))) H4))))))))) H2))) H1)))))))))). -(* COMMENTS -Initial nodes: 673 -END *) +d1 (CHead d0 (Bind b0) w0))).(let TMP_19 \def (S h) in (let TMP_20 \def (Bind +b) in (let TMP_21 \def (CHead d1 TMP_20 w) in (let H_y \def (getl_trans +TMP_19 c1 TMP_21 i H0) in (let TMP_22 \def (S h) in (let TMP_23 \def (plus +TMP_22 i) in (let TMP_24 \def (Bind b0) in (let TMP_25 \def (CHead d0 TMP_24 +w0) in (let TMP_26 \def (Bind b) in (let TMP_27 \def (Bind b0) in (let TMP_28 +\def (CHead d0 TMP_27 w0) in (let TMP_29 \def (getl_head TMP_26 h d1 TMP_28 +H3 w) in (let TMP_30 \def (H_y TMP_25 TMP_29) in (let H_x0 \def (H b0 d0 w0 +TMP_23 TMP_30) in (let H4 \def H_x0 in (let TMP_35 \def (\lambda (d2: C).(let +TMP_31 \def (plus h i) in (let TMP_32 \def (S TMP_31) in (let TMP_33 \def +(Bind b0) in (let TMP_34 \def (CHead d2 TMP_33 w0) in (getl TMP_32 c2 +TMP_34)))))) in (let TMP_38 \def (\lambda (d2: C).(let TMP_36 \def (Bind b0) +in (let TMP_37 \def (CHead d2 TMP_36 w0) in (getl h x TMP_37)))) in (let +TMP_39 \def (ex C TMP_38) in (let TMP_80 \def (\lambda (x0: C).(\lambda (H5: +(getl (S (plus h i)) c2 (CHead x0 (Bind b0) w0))).(let TMP_40 \def (plus h i) +in (let TMP_41 \def (S TMP_40) in (let TMP_42 \def (Bind b0) in (let TMP_43 +\def (CHead x0 TMP_42 w0) in (let TMP_44 \def (Bind b) in (let TMP_45 \def +(CHead x TMP_44 w) in (let H_y0 \def (getl_conf_le TMP_41 TMP_43 c2 H5 TMP_45 +i H2) in (let TMP_46 \def (S h) in (let TMP_47 \def (plus TMP_46 i) in (let +H6 \def (refl_equal nat TMP_47) in (let TMP_48 \def (plus h i) in (let TMP_49 +\def (S TMP_48) in (let TMP_55 \def (\lambda (n: nat).(let TMP_50 \def (minus +n i) in (let TMP_51 \def (Bind b) in (let TMP_52 \def (CHead x TMP_51 w) in +(let TMP_53 \def (Bind b0) in (let TMP_54 \def (CHead x0 TMP_53 w0) in (getl +TMP_50 TMP_52 TMP_54))))))) in (let TMP_56 \def (plus h i) in (let TMP_57 +\def (le_plus_r h i) in (let TMP_58 \def (le_S i TMP_56 TMP_57) in (let +TMP_59 \def (H_y0 TMP_58) in (let TMP_60 \def (S h) in (let TMP_61 \def (plus +TMP_60 i) in (let H7 \def (eq_ind nat TMP_49 TMP_55 TMP_59 TMP_61 H6) in (let +TMP_62 \def (S h) in (let TMP_63 \def (plus TMP_62 i) in (let TMP_64 \def +(minus TMP_63 i) in (let TMP_69 \def (\lambda (n: nat).(let TMP_65 \def (Bind +b) in (let TMP_66 \def (CHead x TMP_65 w) in (let TMP_67 \def (Bind b0) in +(let TMP_68 \def (CHead x0 TMP_67 w0) in (getl n TMP_66 TMP_68)))))) in (let +TMP_70 \def (S h) in (let TMP_71 \def (S h) in (let TMP_72 \def (minus_plus_r +TMP_71 i) in (let H8 \def (eq_ind nat TMP_64 TMP_69 H7 TMP_70 TMP_72) in (let +TMP_75 \def (\lambda (d2: C).(let TMP_73 \def (Bind b0) in (let TMP_74 \def +(CHead d2 TMP_73 w0) in (getl h x TMP_74)))) in (let TMP_76 \def (Bind b) in +(let TMP_77 \def (Bind b0) in (let TMP_78 \def (CHead x0 TMP_77 w0) in (let +TMP_79 \def (getl_gen_S TMP_76 x TMP_78 w h H8) in (ex_intro C TMP_75 x0 +TMP_79)))))))))))))))))))))))))))))))))))) in (ex_ind C TMP_35 TMP_39 TMP_80 +H4))))))))))))))))))))))))) in (ex_intro2 C TMP_15 TMP_18 x TMP_81 H2)))))) +in (ex_ind C TMP_3 TMP_11 TMP_82 H1))))))))))))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/defs.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/defs.ma index 30607a4fc..5428dde7d 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/clear/defs.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/clear/defs.ma @@ -14,7 +14,7 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/C/defs.ma". +include "basic_1/C/defs.ma". inductive clear: C \to (C \to Prop) \def | clear_bind: \forall (b: B).(\forall (e: C).(\forall (u: T).(clear (CHead e diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma index aae3fedc0..a16ba8b23 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/clear/fwd.ma". +include "basic_1/clear/fwd.ma". -include "Basic-1/drop/fwd.ma". +include "basic_1/drop/fwd.ma". theorem drop_clear: \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((drop (S i) O c1 c2) \to @@ -24,88 +24,123 @@ theorem drop_clear: e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2)))))))) \def - \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).(\forall (i: -nat).((drop (S i) O c c2) \to (ex2_3 B C T (\lambda (b: B).(\lambda (e: -C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda -(e: C).(\lambda (_: T).(drop i O e c2))))))))) (\lambda (n: nat).(\lambda -(c2: C).(\lambda (i: nat).(\lambda (H: (drop (S i) O (CSort n) c2)).(and3_ind -(eq C c2 (CSort n)) (eq nat (S i) O) (eq nat O O) (ex2_3 B C T (\lambda (b: -B).(\lambda (e: C).(\lambda (v: T).(clear (CSort n) (CHead e (Bind b) v))))) -(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) (\lambda -(_: (eq C c2 (CSort n))).(\lambda (H1: (eq nat (S i) O)).(\lambda (_: (eq nat -O O)).(let H3 \def (eq_ind nat (S i) (\lambda (ee: nat).(match ee in nat -return (\lambda (_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow -True])) I O H1) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (e: -C).(\lambda (v: T).(clear (CSort n) (CHead e (Bind b) v))))) (\lambda (_: -B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) H3))))) (drop_gen_sort -n (S i) O c2 H)))))) (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall -(i: nat).((drop (S i) O c c2) \to (ex2_3 B C T (\lambda (b: B).(\lambda (e: -C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda -(e: C).(\lambda (_: T).(drop i O e c2)))))))))).(\lambda (k: K).(\lambda (t: -T).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H0: (drop (S i) O (CHead c k -t) c2)).(K_ind (\lambda (k0: K).((drop (r k0 i) O c c2) \to (ex2_3 B C T -(\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c k0 t) (CHead + \lambda (c1: C).(let TMP_5 \def (\lambda (c: C).(\forall (c2: C).(\forall +(i: nat).((drop (S i) O c c2) \to (let TMP_3 \def (\lambda (b: B).(\lambda +(e: C).(\lambda (v: T).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead e +TMP_1 v) in (clear c TMP_2)))))) in (let TMP_4 \def (\lambda (_: B).(\lambda +(e: C).(\lambda (_: T).(drop i O e c2)))) in (ex2_3 B C T TMP_3 TMP_4))))))) +in (let TMP_28 \def (\lambda (n: nat).(\lambda (c2: C).(\lambda (i: +nat).(\lambda (H: (drop (S i) O (CSort n) c2)).(let TMP_6 \def (CSort n) in +(let TMP_7 \def (eq C c2 TMP_6) in (let TMP_8 \def (S i) in (let TMP_9 \def +(eq nat TMP_8 O) in (let TMP_10 \def (eq nat O O) in (let TMP_14 \def +(\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(let TMP_11 \def (CSort n) in +(let TMP_12 \def (Bind b) in (let TMP_13 \def (CHead e TMP_12 v) in (clear +TMP_11 TMP_13))))))) in (let TMP_15 \def (\lambda (_: B).(\lambda (e: +C).(\lambda (_: T).(drop i O e c2)))) in (let TMP_16 \def (ex2_3 B C T TMP_14 +TMP_15) in (let TMP_25 \def (\lambda (_: (eq C c2 (CSort n))).(\lambda (H1: +(eq nat (S i) O)).(\lambda (_: (eq nat O O)).(let TMP_17 \def (S i) in (let +TMP_18 \def (\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) +\Rightarrow True])) in (let H3 \def (eq_ind nat TMP_17 TMP_18 I O H1) in (let +TMP_22 \def (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(let TMP_19 \def +(CSort n) in (let TMP_20 \def (Bind b) in (let TMP_21 \def (CHead e TMP_20 v) +in (clear TMP_19 TMP_21))))))) in (let TMP_23 \def (\lambda (_: B).(\lambda +(e: C).(\lambda (_: T).(drop i O e c2)))) in (let TMP_24 \def (ex2_3 B C T +TMP_22 TMP_23) in (False_ind TMP_24 H3)))))))))) in (let TMP_26 \def (S i) in +(let TMP_27 \def (drop_gen_sort n TMP_26 O c2 H) in (and3_ind TMP_7 TMP_9 +TMP_10 TMP_16 TMP_25 TMP_27)))))))))))))))) in (let TMP_66 \def (\lambda (c: +C).(\lambda (H: ((\forall (c2: C).(\forall (i: nat).((drop (S i) O c c2) \to +(ex2_3 B C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e -c2))))))) (\lambda (b: B).(\lambda (H1: (drop (r (Bind b) i) O c -c2)).(ex2_3_intro B C T (\lambda (b0: B).(\lambda (e: C).(\lambda (v: -T).(clear (CHead c (Bind b) t) (CHead e (Bind b0) v))))) (\lambda (_: -B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2)))) b c t (clear_bind b c -t) H1))) (\lambda (f: F).(\lambda (H1: (drop (r (Flat f) i) O c c2)).(let H2 -\def (H c2 i H1) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda -(v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: -C).(\lambda (_: T).(drop i O e c2)))) (ex2_3 B C T (\lambda (b: B).(\lambda -(e: C).(\lambda (v: T).(clear (CHead c (Flat f) t) (CHead e (Bind b) v))))) -(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) (\lambda -(x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H3: (clear c (CHead x1 -(Bind x0) x2))).(\lambda (H4: (drop i O x1 c2)).(ex2_3_intro B C T (\lambda -(b: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c (Flat f) t) (CHead e -(Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e -c2)))) x0 x1 x2 (clear_flat c (CHead x1 (Bind x0) x2) H3 f t) H4)))))) H2)))) -k (drop_gen_drop k c c2 t i H0))))))))) c1). -(* COMMENTS -Initial nodes: 770 -END *) +c2)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (i: +nat).(\lambda (H0: (drop (S i) O (CHead c k t) c2)).(let TMP_34 \def (\lambda +(k0: K).((drop (r k0 i) O c c2) \to (let TMP_32 \def (\lambda (b: B).(\lambda +(e: C).(\lambda (v: T).(let TMP_29 \def (CHead c k0 t) in (let TMP_30 \def +(Bind b) in (let TMP_31 \def (CHead e TMP_30 v) in (clear TMP_29 +TMP_31))))))) in (let TMP_33 \def (\lambda (_: B).(\lambda (e: C).(\lambda +(_: T).(drop i O e c2)))) in (ex2_3 B C T TMP_32 TMP_33))))) in (let TMP_42 +\def (\lambda (b: B).(\lambda (H1: (drop (r (Bind b) i) O c c2)).(let TMP_39 +\def (\lambda (b0: B).(\lambda (e: C).(\lambda (v: T).(let TMP_35 \def (Bind +b) in (let TMP_36 \def (CHead c TMP_35 t) in (let TMP_37 \def (Bind b0) in +(let TMP_38 \def (CHead e TMP_37 v) in (clear TMP_36 TMP_38)))))))) in (let +TMP_40 \def (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e +c2)))) in (let TMP_41 \def (clear_bind b c t) in (ex2_3_intro B C T TMP_39 +TMP_40 b c t TMP_41 H1)))))) in (let TMP_64 \def (\lambda (f: F).(\lambda +(H1: (drop (r (Flat f) i) O c c2)).(let H2 \def (H c2 i H1) in (let TMP_45 +\def (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(let TMP_43 \def (Bind +b) in (let TMP_44 \def (CHead e TMP_43 v) in (clear c TMP_44)))))) in (let +TMP_46 \def (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e +c2)))) in (let TMP_51 \def (\lambda (b: B).(\lambda (e: C).(\lambda (v: +T).(let TMP_47 \def (Flat f) in (let TMP_48 \def (CHead c TMP_47 t) in (let +TMP_49 \def (Bind b) in (let TMP_50 \def (CHead e TMP_49 v) in (clear TMP_48 +TMP_50)))))))) in (let TMP_52 \def (\lambda (_: B).(\lambda (e: C).(\lambda +(_: T).(drop i O e c2)))) in (let TMP_53 \def (ex2_3 B C T TMP_51 TMP_52) in +(let TMP_63 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda +(H3: (clear c (CHead x1 (Bind x0) x2))).(\lambda (H4: (drop i O x1 c2)).(let +TMP_58 \def (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(let TMP_54 \def +(Flat f) in (let TMP_55 \def (CHead c TMP_54 t) in (let TMP_56 \def (Bind b) +in (let TMP_57 \def (CHead e TMP_56 v) in (clear TMP_55 TMP_57)))))))) in +(let TMP_59 \def (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e +c2)))) in (let TMP_60 \def (Bind x0) in (let TMP_61 \def (CHead x1 TMP_60 x2) +in (let TMP_62 \def (clear_flat c TMP_61 H3 f t) in (ex2_3_intro B C T TMP_58 +TMP_59 x0 x1 x2 TMP_62 H4))))))))))) in (ex2_3_ind B C T TMP_45 TMP_46 TMP_53 +TMP_63 H2)))))))))) in (let TMP_65 \def (drop_gen_drop k c c2 t i H0) in +(K_ind TMP_34 TMP_42 TMP_64 k TMP_65)))))))))))) in (C_ind TMP_5 TMP_28 +TMP_66 c1)))). theorem drop_clear_O: \forall (b: B).(\forall (c: C).(\forall (e1: C).(\forall (u: T).((clear c (CHead e1 (Bind b) u)) \to (\forall (e2: C).(\forall (i: nat).((drop i O e1 e2) \to (drop (S i) O c e2)))))))) \def - \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e1: -C).(\forall (u: T).((clear c0 (CHead e1 (Bind b) u)) \to (\forall (e2: -C).(\forall (i: nat).((drop i O e1 e2) \to (drop (S i) O c0 e2)))))))) -(\lambda (n: nat).(\lambda (e1: C).(\lambda (u: T).(\lambda (H: (clear (CSort -n) (CHead e1 (Bind b) u))).(\lambda (e2: C).(\lambda (i: nat).(\lambda (_: -(drop i O e1 e2)).(clear_gen_sort (CHead e1 (Bind b) u) n H (drop (S i) O -(CSort n) e2))))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e1: -C).(\forall (u: T).((clear c0 (CHead e1 (Bind b) u)) \to (\forall (e2: -C).(\forall (i: nat).((drop i O e1 e2) \to (drop (S i) O c0 -e2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e1: C).(\lambda (u: -T).(\lambda (H0: (clear (CHead c0 k t) (CHead e1 (Bind b) u))).(\lambda (e2: -C).(\lambda (i: nat).(\lambda (H1: (drop i O e1 e2)).(K_ind (\lambda (k0: -K).((clear (CHead c0 k0 t) (CHead e1 (Bind b) u)) \to (drop (S i) O (CHead c0 -k0 t) e2))) (\lambda (b0: B).(\lambda (H2: (clear (CHead c0 (Bind b0) t) -(CHead e1 (Bind b) u))).(let H3 \def (f_equal C C (\lambda (e: C).(match e in -C return (\lambda (_: C).C) with [(CSort _) \Rightarrow e1 | (CHead c1 _ _) -\Rightarrow c1])) (CHead e1 (Bind b) u) (CHead c0 (Bind b0) t) -(clear_gen_bind b0 c0 (CHead e1 (Bind b) u) t H2)) in ((let H4 \def (f_equal -C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) -\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: -K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e1 -(Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 (Bind b) -u) t H2)) in ((let H5 \def (f_equal C T (\lambda (e: C).(match e in C return -(\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow -t0])) (CHead e1 (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 -(CHead e1 (Bind b) u) t H2)) in (\lambda (H6: (eq B b b0)).(\lambda (H7: (eq -C e1 c0)).(let H8 \def (eq_ind C e1 (\lambda (c1: C).(drop i O c1 e2)) H1 c0 -H7) in (eq_ind B b (\lambda (b1: B).(drop (S i) O (CHead c0 (Bind b1) t) e2)) -(drop_drop (Bind b) i c0 e2 H8 t) b0 H6))))) H4)) H3)))) (\lambda (f: -F).(\lambda (H2: (clear (CHead c0 (Flat f) t) (CHead e1 (Bind b) -u))).(drop_drop (Flat f) i c0 e2 (H e1 u (clear_gen_flat f c0 (CHead e1 (Bind -b) u) t H2) e2 i H1) t))) k H0))))))))))) c)). -(* COMMENTS -Initial nodes: 619 -END *) + \lambda (b: B).(\lambda (c: C).(let TMP_2 \def (\lambda (c0: C).(\forall +(e1: C).(\forall (u: T).((clear c0 (CHead e1 (Bind b) u)) \to (\forall (e2: +C).(\forall (i: nat).((drop i O e1 e2) \to (let TMP_1 \def (S i) in (drop +TMP_1 O c0 e2))))))))) in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: +C).(\lambda (u: T).(\lambda (H: (clear (CSort n) (CHead e1 (Bind b) +u))).(\lambda (e2: C).(\lambda (i: nat).(\lambda (_: (drop i O e1 e2)).(let +TMP_3 \def (Bind b) in (let TMP_4 \def (CHead e1 TMP_3 u) in (let TMP_5 \def +(S i) in (let TMP_6 \def (CSort n) in (let TMP_7 \def (drop TMP_5 O TMP_6 e2) +in (clear_gen_sort TMP_4 n H TMP_7))))))))))))) in (let TMP_52 \def (\lambda +(c0: C).(\lambda (H: ((\forall (e1: C).(\forall (u: T).((clear c0 (CHead e1 +(Bind b) u)) \to (\forall (e2: C).(\forall (i: nat).((drop i O e1 e2) \to +(drop (S i) O c0 e2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e1: +C).(\lambda (u: T).(\lambda (H0: (clear (CHead c0 k t) (CHead e1 (Bind b) +u))).(\lambda (e2: C).(\lambda (i: nat).(\lambda (H1: (drop i O e1 e2)).(let +TMP_11 \def (\lambda (k0: K).((clear (CHead c0 k0 t) (CHead e1 (Bind b) u)) +\to (let TMP_9 \def (S i) in (let TMP_10 \def (CHead c0 k0 t) in (drop TMP_9 +O TMP_10 e2))))) in (let TMP_45 \def (\lambda (b0: B).(\lambda (H2: (clear +(CHead c0 (Bind b0) t) (CHead e1 (Bind b) u))).(let TMP_12 \def (\lambda (e: +C).(match e with [(CSort _) \Rightarrow e1 | (CHead c1 _ _) \Rightarrow c1])) +in (let TMP_13 \def (Bind b) in (let TMP_14 \def (CHead e1 TMP_13 u) in (let +TMP_15 \def (Bind b0) in (let TMP_16 \def (CHead c0 TMP_15 t) in (let TMP_17 +\def (Bind b) in (let TMP_18 \def (CHead e1 TMP_17 u) in (let TMP_19 \def +(clear_gen_bind b0 c0 TMP_18 t H2) in (let H3 \def (f_equal C C TMP_12 TMP_14 +TMP_16 TMP_19) in (let TMP_20 \def (\lambda (e: C).(match e with [(CSort _) +\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1) +\Rightarrow b1 | (Flat _) \Rightarrow b])])) in (let TMP_21 \def (Bind b) in +(let TMP_22 \def (CHead e1 TMP_21 u) in (let TMP_23 \def (Bind b0) in (let +TMP_24 \def (CHead c0 TMP_23 t) in (let TMP_25 \def (Bind b) in (let TMP_26 +\def (CHead e1 TMP_25 u) in (let TMP_27 \def (clear_gen_bind b0 c0 TMP_26 t +H2) in (let H4 \def (f_equal C B TMP_20 TMP_22 TMP_24 TMP_27) in (let TMP_28 +\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t0) +\Rightarrow t0])) in (let TMP_29 \def (Bind b) in (let TMP_30 \def (CHead e1 +TMP_29 u) in (let TMP_31 \def (Bind b0) in (let TMP_32 \def (CHead c0 TMP_31 +t) in (let TMP_33 \def (Bind b) in (let TMP_34 \def (CHead e1 TMP_33 u) in +(let TMP_35 \def (clear_gen_bind b0 c0 TMP_34 t H2) in (let H5 \def (f_equal +C T TMP_28 TMP_30 TMP_32 TMP_35) in (let TMP_43 \def (\lambda (H6: (eq B b +b0)).(\lambda (H7: (eq C e1 c0)).(let TMP_36 \def (\lambda (c1: C).(drop i O +c1 e2)) in (let H8 \def (eq_ind C e1 TMP_36 H1 c0 H7) in (let TMP_40 \def +(\lambda (b1: B).(let TMP_37 \def (S i) in (let TMP_38 \def (Bind b1) in (let +TMP_39 \def (CHead c0 TMP_38 t) in (drop TMP_37 O TMP_39 e2))))) in (let +TMP_41 \def (Bind b) in (let TMP_42 \def (drop_drop TMP_41 i c0 e2 H8 t) in +(eq_ind B b TMP_40 TMP_42 b0 H6)))))))) in (let TMP_44 \def (TMP_43 H4) in +(TMP_44 H3)))))))))))))))))))))))))))))))) in (let TMP_51 \def (\lambda (f: +F).(\lambda (H2: (clear (CHead c0 (Flat f) t) (CHead e1 (Bind b) u))).(let +TMP_46 \def (Flat f) in (let TMP_47 \def (Bind b) in (let TMP_48 \def (CHead +e1 TMP_47 u) in (let TMP_49 \def (clear_gen_flat f c0 TMP_48 t H2) in (let +TMP_50 \def (H e1 u TMP_49 e2 i H1) in (drop_drop TMP_46 i c0 e2 TMP_50 +t)))))))) in (K_ind TMP_11 TMP_45 TMP_51 k H0)))))))))))))) in (C_ind TMP_2 +TMP_8 TMP_52 c))))). theorem drop_clear_S: \forall (x2: C).(\forall (x1: C).(\forall (h: nat).(\forall (d: nat).((drop @@ -113,69 +148,126 @@ h (S d) x1 x2) \to (\forall (b: B).(\forall (c2: C).(\forall (u: T).((clear x2 (CHead c2 (Bind b) u)) \to (ex2 C (\lambda (c1: C).(clear x1 (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2))))))))))) \def - \lambda (x2: C).(C_ind (\lambda (c: C).(\forall (x1: C).(\forall (h: -nat).(\forall (d: nat).((drop h (S d) x1 c) \to (\forall (b: B).(\forall (c2: -C).(\forall (u: T).((clear c (CHead c2 (Bind b) u)) \to (ex2 C (\lambda (c1: -C).(clear x1 (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 -c2)))))))))))) (\lambda (n: nat).(\lambda (x1: C).(\lambda (h: nat).(\lambda -(d: nat).(\lambda (_: (drop h (S d) x1 (CSort n))).(\lambda (b: B).(\lambda -(c2: C).(\lambda (u: T).(\lambda (H0: (clear (CSort n) (CHead c2 (Bind b) -u))).(clear_gen_sort (CHead c2 (Bind b) u) n H0 (ex2 C (\lambda (c1: -C).(clear x1 (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 -c2))))))))))))) (\lambda (c: C).(\lambda (H: ((\forall (x1: C).(\forall (h: -nat).(\forall (d: nat).((drop h (S d) x1 c) \to (\forall (b: B).(\forall (c2: -C).(\forall (u: T).((clear c (CHead c2 (Bind b) u)) \to (ex2 C (\lambda (c1: -C).(clear x1 (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 -c2))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (x1: C).(\lambda (h: -nat).(\lambda (d: nat).(\lambda (H0: (drop h (S d) x1 (CHead c k -t))).(\lambda (b: B).(\lambda (c2: C).(\lambda (u: T).(\lambda (H1: (clear -(CHead c k t) (CHead c2 (Bind b) u))).(ex2_ind C (\lambda (e: C).(eq C x1 -(CHead e k (lift h (r k d) t)))) (\lambda (e: C).(drop h (r k d) e c)) (ex2 C -(\lambda (c1: C).(clear x1 (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: -C).(drop h d c1 c2))) (\lambda (x: C).(\lambda (H2: (eq C x1 (CHead x k (lift -h (r k d) t)))).(\lambda (H3: (drop h (r k d) x c)).(eq_ind_r C (CHead x k -(lift h (r k d) t)) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(clear c0 (CHead -c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2)))) (K_ind -(\lambda (k0: K).((clear (CHead c k0 t) (CHead c2 (Bind b) u)) \to ((drop h -(r k0 d) x c) \to (ex2 C (\lambda (c1: C).(clear (CHead x k0 (lift h (r k0 d) -t)) (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2)))))) -(\lambda (b0: B).(\lambda (H4: (clear (CHead c (Bind b0) t) (CHead c2 (Bind -b) u))).(\lambda (H5: (drop h (r (Bind b0) d) x c)).(let H6 \def (f_equal C C -(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) -\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u) -(CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in -((let H7 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: -C).B) with [(CSort _) \Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 in -K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) -\Rightarrow b])])) (CHead c2 (Bind b) u) (CHead c (Bind b0) t) -(clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in ((let H8 \def (f_equal C -T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) -\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead c2 (Bind b) u) (CHead -c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in (\lambda -(H9: (eq B b b0)).(\lambda (H10: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: -T).(ex2 C (\lambda (c1: C).(clear (CHead x (Bind b0) (lift h (r (Bind b0) d) -t)) (CHead c1 (Bind b) (lift h d t0)))) (\lambda (c1: C).(drop h d c1 c2)))) -(eq_ind_r C c (\lambda (c0: C).(ex2 C (\lambda (c1: C).(clear (CHead x (Bind -b0) (lift h (r (Bind b0) d) t)) (CHead c1 (Bind b) (lift h d t)))) (\lambda -(c1: C).(drop h d c1 c0)))) (eq_ind_r B b0 (\lambda (b1: B).(ex2 C (\lambda -(c1: C).(clear (CHead x (Bind b0) (lift h (r (Bind b0) d) t)) (CHead c1 (Bind -b1) (lift h d t)))) (\lambda (c1: C).(drop h d c1 c)))) (ex_intro2 C (\lambda -(c1: C).(clear (CHead x (Bind b0) (lift h (r (Bind b0) d) t)) (CHead c1 (Bind -b0) (lift h d t)))) (\lambda (c1: C).(drop h d c1 c)) x (clear_bind b0 x -(lift h d t)) H5) b H9) c2 H10) u H8)))) H7)) H6))))) (\lambda (f: + \lambda (x2: C).(let TMP_6 \def (\lambda (c: C).(\forall (x1: C).(\forall +(h: nat).(\forall (d: nat).((drop h (S d) x1 c) \to (\forall (b: B).(\forall +(c2: C).(\forall (u: T).((clear c (CHead c2 (Bind b) u)) \to (let TMP_4 \def +(\lambda (c1: C).(let TMP_1 \def (Bind b) in (let TMP_2 \def (lift h d u) in +(let TMP_3 \def (CHead c1 TMP_1 TMP_2) in (clear x1 TMP_3))))) in (let TMP_5 +\def (\lambda (c1: C).(drop h d c1 c2)) in (ex2 C TMP_4 TMP_5)))))))))))) in +(let TMP_15 \def (\lambda (n: nat).(\lambda (x1: C).(\lambda (h: +nat).(\lambda (d: nat).(\lambda (_: (drop h (S d) x1 (CSort n))).(\lambda (b: +B).(\lambda (c2: C).(\lambda (u: T).(\lambda (H0: (clear (CSort n) (CHead c2 +(Bind b) u))).(let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead c2 TMP_7 u) +in (let TMP_12 \def (\lambda (c1: C).(let TMP_9 \def (Bind b) in (let TMP_10 +\def (lift h d u) in (let TMP_11 \def (CHead c1 TMP_9 TMP_10) in (clear x1 +TMP_11))))) in (let TMP_13 \def (\lambda (c1: C).(drop h d c1 c2)) in (let +TMP_14 \def (ex2 C TMP_12 TMP_13) in (clear_gen_sort TMP_8 n H0 +TMP_14))))))))))))))) in (let TMP_162 \def (\lambda (c: C).(\lambda (H: +((\forall (x1: C).(\forall (h: nat).(\forall (d: nat).((drop h (S d) x1 c) +\to (\forall (b: B).(\forall (c2: C).(\forall (u: T).((clear c (CHead c2 +(Bind b) u)) \to (ex2 C (\lambda (c1: C).(clear x1 (CHead c1 (Bind b) (lift h +d u)))) (\lambda (c1: C).(drop h d c1 c2))))))))))))).(\lambda (k: +K).(\lambda (t: T).(\lambda (x1: C).(\lambda (h: nat).(\lambda (d: +nat).(\lambda (H0: (drop h (S d) x1 (CHead c k t))).(\lambda (b: B).(\lambda +(c2: C).(\lambda (u: T).(\lambda (H1: (clear (CHead c k t) (CHead c2 (Bind b) +u))).(let TMP_19 \def (\lambda (e: C).(let TMP_16 \def (r k d) in (let TMP_17 +\def (lift h TMP_16 t) in (let TMP_18 \def (CHead e k TMP_17) in (eq C x1 +TMP_18))))) in (let TMP_21 \def (\lambda (e: C).(let TMP_20 \def (r k d) in +(drop h TMP_20 e c))) in (let TMP_25 \def (\lambda (c1: C).(let TMP_22 \def +(Bind b) in (let TMP_23 \def (lift h d u) in (let TMP_24 \def (CHead c1 +TMP_22 TMP_23) in (clear x1 TMP_24))))) in (let TMP_26 \def (\lambda (c1: +C).(drop h d c1 c2)) in (let TMP_27 \def (ex2 C TMP_25 TMP_26) in (let +TMP_160 \def (\lambda (x: C).(\lambda (H2: (eq C x1 (CHead x k (lift h (r k +d) t)))).(\lambda (H3: (drop h (r k d) x c)).(let TMP_28 \def (r k d) in (let +TMP_29 \def (lift h TMP_28 t) in (let TMP_30 \def (CHead x k TMP_29) in (let +TMP_36 \def (\lambda (c0: C).(let TMP_34 \def (\lambda (c1: C).(let TMP_31 +\def (Bind b) in (let TMP_32 \def (lift h d u) in (let TMP_33 \def (CHead c1 +TMP_31 TMP_32) in (clear c0 TMP_33))))) in (let TMP_35 \def (\lambda (c1: +C).(drop h d c1 c2)) in (ex2 C TMP_34 TMP_35)))) in (let TMP_45 \def (\lambda +(k0: K).((clear (CHead c k0 t) (CHead c2 (Bind b) u)) \to ((drop h (r k0 d) x +c) \to (let TMP_43 \def (\lambda (c1: C).(let TMP_37 \def (r k0 d) in (let +TMP_38 \def (lift h TMP_37 t) in (let TMP_39 \def (CHead x k0 TMP_38) in (let +TMP_40 \def (Bind b) in (let TMP_41 \def (lift h d u) in (let TMP_42 \def +(CHead c1 TMP_40 TMP_41) in (clear TMP_39 TMP_42)))))))) in (let TMP_44 \def +(\lambda (c1: C).(drop h d c1 c2)) in (ex2 C TMP_43 TMP_44)))))) in (let +TMP_120 \def (\lambda (b0: B).(\lambda (H4: (clear (CHead c (Bind b0) t) +(CHead c2 (Bind b) u))).(\lambda (H5: (drop h (r (Bind b0) d) x c)).(let +TMP_46 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead +c0 _ _) \Rightarrow c0])) in (let TMP_47 \def (Bind b) in (let TMP_48 \def +(CHead c2 TMP_47 u) in (let TMP_49 \def (Bind b0) in (let TMP_50 \def (CHead +c TMP_49 t) in (let TMP_51 \def (Bind b) in (let TMP_52 \def (CHead c2 TMP_51 +u) in (let TMP_53 \def (clear_gen_bind b0 c TMP_52 t H4) in (let H6 \def +(f_equal C C TMP_46 TMP_48 TMP_50 TMP_53) in (let TMP_54 \def (\lambda (e: +C).(match e with [(CSort _) \Rightarrow b | (CHead _ k0 _) \Rightarrow (match +k0 with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) in (let +TMP_55 \def (Bind b) in (let TMP_56 \def (CHead c2 TMP_55 u) in (let TMP_57 +\def (Bind b0) in (let TMP_58 \def (CHead c TMP_57 t) in (let TMP_59 \def +(Bind b) in (let TMP_60 \def (CHead c2 TMP_59 u) in (let TMP_61 \def +(clear_gen_bind b0 c TMP_60 t H4) in (let H7 \def (f_equal C B TMP_54 TMP_56 +TMP_58 TMP_61) in (let TMP_62 \def (\lambda (e: C).(match e with [(CSort _) +\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_63 \def (Bind b) +in (let TMP_64 \def (CHead c2 TMP_63 u) in (let TMP_65 \def (Bind b0) in (let +TMP_66 \def (CHead c TMP_65 t) in (let TMP_67 \def (Bind b) in (let TMP_68 +\def (CHead c2 TMP_67 u) in (let TMP_69 \def (clear_gen_bind b0 c TMP_68 t +H4) in (let H8 \def (f_equal C T TMP_62 TMP_64 TMP_66 TMP_69) in (let TMP_118 +\def (\lambda (H9: (eq B b b0)).(\lambda (H10: (eq C c2 c)).(let TMP_80 \def +(\lambda (t0: T).(let TMP_78 \def (\lambda (c1: C).(let TMP_70 \def (Bind b0) +in (let TMP_71 \def (Bind b0) in (let TMP_72 \def (r TMP_71 d) in (let TMP_73 +\def (lift h TMP_72 t) in (let TMP_74 \def (CHead x TMP_70 TMP_73) in (let +TMP_75 \def (Bind b) in (let TMP_76 \def (lift h d t0) in (let TMP_77 \def +(CHead c1 TMP_75 TMP_76) in (clear TMP_74 TMP_77)))))))))) in (let TMP_79 +\def (\lambda (c1: C).(drop h d c1 c2)) in (ex2 C TMP_78 TMP_79)))) in (let +TMP_91 \def (\lambda (c0: C).(let TMP_89 \def (\lambda (c1: C).(let TMP_81 +\def (Bind b0) in (let TMP_82 \def (Bind b0) in (let TMP_83 \def (r TMP_82 d) +in (let TMP_84 \def (lift h TMP_83 t) in (let TMP_85 \def (CHead x TMP_81 +TMP_84) in (let TMP_86 \def (Bind b) in (let TMP_87 \def (lift h d t) in (let +TMP_88 \def (CHead c1 TMP_86 TMP_87) in (clear TMP_85 TMP_88)))))))))) in +(let TMP_90 \def (\lambda (c1: C).(drop h d c1 c0)) in (ex2 C TMP_89 +TMP_90)))) in (let TMP_102 \def (\lambda (b1: B).(let TMP_100 \def (\lambda +(c1: C).(let TMP_92 \def (Bind b0) in (let TMP_93 \def (Bind b0) in (let +TMP_94 \def (r TMP_93 d) in (let TMP_95 \def (lift h TMP_94 t) in (let TMP_96 +\def (CHead x TMP_92 TMP_95) in (let TMP_97 \def (Bind b1) in (let TMP_98 +\def (lift h d t) in (let TMP_99 \def (CHead c1 TMP_97 TMP_98) in (clear +TMP_96 TMP_99)))))))))) in (let TMP_101 \def (\lambda (c1: C).(drop h d c1 +c)) in (ex2 C TMP_100 TMP_101)))) in (let TMP_111 \def (\lambda (c1: C).(let +TMP_103 \def (Bind b0) in (let TMP_104 \def (Bind b0) in (let TMP_105 \def (r +TMP_104 d) in (let TMP_106 \def (lift h TMP_105 t) in (let TMP_107 \def +(CHead x TMP_103 TMP_106) in (let TMP_108 \def (Bind b0) in (let TMP_109 \def +(lift h d t) in (let TMP_110 \def (CHead c1 TMP_108 TMP_109) in (clear +TMP_107 TMP_110)))))))))) in (let TMP_112 \def (\lambda (c1: C).(drop h d c1 +c)) in (let TMP_113 \def (lift h d t) in (let TMP_114 \def (clear_bind b0 x +TMP_113) in (let TMP_115 \def (ex_intro2 C TMP_111 TMP_112 x TMP_114 H5) in +(let TMP_116 \def (eq_ind_r B b0 TMP_102 TMP_115 b H9) in (let TMP_117 \def +(eq_ind_r C c TMP_91 TMP_116 c2 H10) in (eq_ind_r T t TMP_80 TMP_117 u +H8))))))))))))) in (let TMP_119 \def (TMP_118 H7) in (TMP_119 +H6))))))))))))))))))))))))))))))))) in (let TMP_158 \def (\lambda (f: F).(\lambda (H4: (clear (CHead c (Flat f) t) (CHead c2 (Bind b) u))).(\lambda -(H5: (drop h (r (Flat f) d) x c)).(let H6 \def (H x h d H5 b c2 u -(clear_gen_flat f c (CHead c2 (Bind b) u) t H4)) in (ex2_ind C (\lambda (c1: -C).(clear x (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 -c2)) (ex2 C (\lambda (c1: C).(clear (CHead x (Flat f) (lift h (r (Flat f) d) -t)) (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2))) +(H5: (drop h (r (Flat f) d) x c)).(let TMP_121 \def (Bind b) in (let TMP_122 +\def (CHead c2 TMP_121 u) in (let TMP_123 \def (clear_gen_flat f c TMP_122 t +H4) in (let H6 \def (H x h d H5 b c2 u TMP_123) in (let TMP_127 \def (\lambda +(c1: C).(let TMP_124 \def (Bind b) in (let TMP_125 \def (lift h d u) in (let +TMP_126 \def (CHead c1 TMP_124 TMP_125) in (clear x TMP_126))))) in (let +TMP_128 \def (\lambda (c1: C).(drop h d c1 c2)) in (let TMP_137 \def (\lambda +(c1: C).(let TMP_129 \def (Flat f) in (let TMP_130 \def (Flat f) in (let +TMP_131 \def (r TMP_130 d) in (let TMP_132 \def (lift h TMP_131 t) in (let +TMP_133 \def (CHead x TMP_129 TMP_132) in (let TMP_134 \def (Bind b) in (let +TMP_135 \def (lift h d u) in (let TMP_136 \def (CHead c1 TMP_134 TMP_135) in +(clear TMP_133 TMP_136)))))))))) in (let TMP_138 \def (\lambda (c1: C).(drop +h d c1 c2)) in (let TMP_139 \def (ex2 C TMP_137 TMP_138) in (let TMP_157 \def (\lambda (x0: C).(\lambda (H7: (clear x (CHead x0 (Bind b) (lift h d -u)))).(\lambda (H8: (drop h d x0 c2)).(ex_intro2 C (\lambda (c1: C).(clear -(CHead x (Flat f) (lift h (r (Flat f) d) t)) (CHead c1 (Bind b) (lift h d -u)))) (\lambda (c1: C).(drop h d c1 c2)) x0 (clear_flat x (CHead x0 (Bind b) -(lift h d u)) H7 f (lift h (r (Flat f) d) t)) H8)))) H6))))) k H1 H3) x1 -H2)))) (drop_gen_skip_r c x1 t h d k H0)))))))))))))) x2). -(* COMMENTS -Initial nodes: 1449 -END *) +u)))).(\lambda (H8: (drop h d x0 c2)).(let TMP_148 \def (\lambda (c1: C).(let +TMP_140 \def (Flat f) in (let TMP_141 \def (Flat f) in (let TMP_142 \def (r +TMP_141 d) in (let TMP_143 \def (lift h TMP_142 t) in (let TMP_144 \def +(CHead x TMP_140 TMP_143) in (let TMP_145 \def (Bind b) in (let TMP_146 \def +(lift h d u) in (let TMP_147 \def (CHead c1 TMP_145 TMP_146) in (clear +TMP_144 TMP_147)))))))))) in (let TMP_149 \def (\lambda (c1: C).(drop h d c1 +c2)) in (let TMP_150 \def (Bind b) in (let TMP_151 \def (lift h d u) in (let +TMP_152 \def (CHead x0 TMP_150 TMP_151) in (let TMP_153 \def (Flat f) in (let +TMP_154 \def (r TMP_153 d) in (let TMP_155 \def (lift h TMP_154 t) in (let +TMP_156 \def (clear_flat x TMP_152 H7 f TMP_155) in (ex_intro2 C TMP_148 +TMP_149 x0 TMP_156 H8))))))))))))) in (ex2_ind C TMP_127 TMP_128 TMP_139 +TMP_157 H6)))))))))))))) in (let TMP_159 \def (K_ind TMP_45 TMP_120 TMP_158 k +H1 H3) in (eq_ind_r C TMP_30 TMP_36 TMP_159 x1 H2)))))))))))) in (let TMP_161 +\def (drop_gen_skip_r c x1 t h d k H0) in (ex2_ind C TMP_19 TMP_21 TMP_27 +TMP_160 TMP_161)))))))))))))))))))) in (C_ind TMP_6 TMP_15 TMP_162 x2)))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/fwd.ma index d64ff77be..5d602754d 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/clear/fwd.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/clear/fwd.ma @@ -14,151 +14,259 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/clear/defs.ma". +include "basic_1/clear/defs.ma". + +include "basic_1/C/fwd.ma". + +let rec clear_ind (P: (C \to (C \to Prop))) (f: (\forall (b: B).(\forall (e: +C).(\forall (u: T).(P (CHead e (Bind b) u) (CHead e (Bind b) u)))))) (f0: +(\forall (e: C).(\forall (c: C).((clear e c) \to ((P e c) \to (\forall (f0: +F).(\forall (u: T).(P (CHead e (Flat f0) u) c)))))))) (c: C) (c0: C) (c1: +clear c c0) on c1: P c c0 \def match c1 with [(clear_bind b e u) \Rightarrow +(f b e u) | (clear_flat e c2 c3 f1 u) \Rightarrow (let TMP_1 \def ((clear_ind +P f f0) e c2 c3) in (f0 e c2 c3 TMP_1 f1 u))]. theorem clear_gen_sort: \forall (x: C).(\forall (n: nat).((clear (CSort n) x) \to (\forall (P: Prop).P))) \def \lambda (x: C).(\lambda (n: nat).(\lambda (H: (clear (CSort n) x)).(\lambda -(P: Prop).(insert_eq C (CSort n) (\lambda (c: C).(clear c x)) (\lambda (_: -C).P) (\lambda (y: C).(\lambda (H0: (clear y x)).(clear_ind (\lambda (c: -C).(\lambda (_: C).((eq C c (CSort n)) \to P))) (\lambda (b: B).(\lambda (e: -C).(\lambda (u: T).(\lambda (H1: (eq C (CHead e (Bind b) u) (CSort n))).(let -H2 \def (eq_ind C (CHead e (Bind b) u) (\lambda (ee: C).(match ee in C return -(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ _ _) -\Rightarrow True])) I (CSort n) H1) in (False_ind P H2)))))) (\lambda (e: -C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (_: (((eq C e (CSort -n)) \to P))).(\lambda (f: F).(\lambda (u: T).(\lambda (H3: (eq C (CHead e -(Flat f) u) (CSort n))).(let H4 \def (eq_ind C (CHead e (Flat f) u) (\lambda -(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) -\Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n) H3) in -(False_ind P H4))))))))) y x H0))) H)))). -(* COMMENTS -Initial nodes: 215 -END *) +(P: Prop).(let TMP_1 \def (CSort n) in (let TMP_2 \def (\lambda (c: C).(clear +c x)) in (let TMP_3 \def (\lambda (_: C).P) in (let TMP_15 \def (\lambda (y: +C).(\lambda (H0: (clear y x)).(let TMP_4 \def (\lambda (c: C).(\lambda (_: +C).((eq C c (CSort n)) \to P))) in (let TMP_9 \def (\lambda (b: B).(\lambda +(e: C).(\lambda (u: T).(\lambda (H1: (eq C (CHead e (Bind b) u) (CSort +n))).(let TMP_5 \def (Bind b) in (let TMP_6 \def (CHead e TMP_5 u) in (let +TMP_7 \def (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | +(CHead _ _ _) \Rightarrow True])) in (let TMP_8 \def (CSort n) in (let H2 +\def (eq_ind C TMP_6 TMP_7 I TMP_8 H1) in (False_ind P H2)))))))))) in (let +TMP_14 \def (\lambda (e: C).(\lambda (c: C).(\lambda (_: (clear e +c)).(\lambda (_: (((eq C e (CSort n)) \to P))).(\lambda (f: F).(\lambda (u: +T).(\lambda (H3: (eq C (CHead e (Flat f) u) (CSort n))).(let TMP_10 \def +(Flat f) in (let TMP_11 \def (CHead e TMP_10 u) in (let TMP_12 \def (\lambda +(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ _ _) +\Rightarrow True])) in (let TMP_13 \def (CSort n) in (let H4 \def (eq_ind C +TMP_11 TMP_12 I TMP_13 H3) in (False_ind P H4))))))))))))) in (clear_ind +TMP_4 TMP_9 TMP_14 y x H0)))))) in (insert_eq C TMP_1 TMP_2 TMP_3 TMP_15 +H)))))))). theorem clear_gen_bind: \forall (b: B).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear (CHead e (Bind b) u) x) \to (eq C x (CHead e (Bind b) u)))))) \def \lambda (b: B).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: -(clear (CHead e (Bind b) u) x)).(insert_eq C (CHead e (Bind b) u) (\lambda -(c: C).(clear c x)) (\lambda (c: C).(eq C x c)) (\lambda (y: C).(\lambda (H0: -(clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead e -(Bind b) u)) \to (eq C c0 c)))) (\lambda (b0: B).(\lambda (e0: C).(\lambda -(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b0) u0) (CHead e (Bind b) -u))).(let H2 \def (f_equal C C (\lambda (e1: C).(match e1 in C return -(\lambda (_: C).C) with [(CSort _) \Rightarrow e0 | (CHead c _ _) \Rightarrow -c])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H3 \def -(f_equal C B (\lambda (e1: C).(match e1 in C return (\lambda (_: C).B) with -[(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow (match k in K return -(\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow -b0])])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H4 \def -(f_equal C T (\lambda (e1: C).(match e1 in C return (\lambda (_: C).T) with -[(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead e0 (Bind -b0) u0) (CHead e (Bind b) u) H1) in (\lambda (H5: (eq B b0 b)).(\lambda (H6: -(eq C e0 e)).(eq_ind_r T u (\lambda (t: T).(eq C (CHead e0 (Bind b0) t) -(CHead e0 (Bind b0) t))) (eq_ind_r C e (\lambda (c: C).(eq C (CHead c (Bind -b0) u) (CHead c (Bind b0) u))) (eq_ind_r B b (\lambda (b1: B).(eq C (CHead e -(Bind b1) u) (CHead e (Bind b1) u))) (refl_equal C (CHead e (Bind b) u)) b0 -H5) e0 H6) u0 H4)))) H3)) H2)))))) (\lambda (e0: C).(\lambda (c: C).(\lambda -(_: (clear e0 c)).(\lambda (_: (((eq C e0 (CHead e (Bind b) u)) \to (eq C c -e0)))).(\lambda (f: F).(\lambda (u0: T).(\lambda (H3: (eq C (CHead e0 (Flat -f) u0) (CHead e (Bind b) u))).(let H4 \def (eq_ind C (CHead e0 (Flat f) u0) -(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) -\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda -(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow -True])])) I (CHead e (Bind b) u) H3) in (False_ind (eq C c (CHead e0 (Flat f) -u0)) H4))))))))) y x H0))) H))))). -(* COMMENTS -Initial nodes: 525 -END *) +(clear (CHead e (Bind b) u) x)).(let TMP_1 \def (Bind b) in (let TMP_2 \def +(CHead e TMP_1 u) in (let TMP_3 \def (\lambda (c: C).(clear c x)) in (let +TMP_4 \def (\lambda (c: C).(eq C x c)) in (let TMP_53 \def (\lambda (y: +C).(\lambda (H0: (clear y x)).(let TMP_5 \def (\lambda (c: C).(\lambda (c0: +C).((eq C c (CHead e (Bind b) u)) \to (eq C c0 c)))) in (let TMP_43 \def +(\lambda (b0: B).(\lambda (e0: C).(\lambda (u0: T).(\lambda (H1: (eq C (CHead +e0 (Bind b0) u0) (CHead e (Bind b) u))).(let TMP_6 \def (\lambda (e1: +C).(match e1 with [(CSort _) \Rightarrow e0 | (CHead c _ _) \Rightarrow c])) +in (let TMP_7 \def (Bind b0) in (let TMP_8 \def (CHead e0 TMP_7 u0) in (let +TMP_9 \def (Bind b) in (let TMP_10 \def (CHead e TMP_9 u) in (let H2 \def +(f_equal C C TMP_6 TMP_8 TMP_10 H1) in (let TMP_11 \def (\lambda (e1: +C).(match e1 with [(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow +(match k with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b0])])) in +(let TMP_12 \def (Bind b0) in (let TMP_13 \def (CHead e0 TMP_12 u0) in (let +TMP_14 \def (Bind b) in (let TMP_15 \def (CHead e TMP_14 u) in (let H3 \def +(f_equal C B TMP_11 TMP_13 TMP_15 H1) in (let TMP_16 \def (\lambda (e1: +C).(match e1 with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) +in (let TMP_17 \def (Bind b0) in (let TMP_18 \def (CHead e0 TMP_17 u0) in +(let TMP_19 \def (Bind b) in (let TMP_20 \def (CHead e TMP_19 u) in (let H4 +\def (f_equal C T TMP_16 TMP_18 TMP_20 H1) in (let TMP_41 \def (\lambda (H5: +(eq B b0 b)).(\lambda (H6: (eq C e0 e)).(let TMP_25 \def (\lambda (t: T).(let +TMP_21 \def (Bind b0) in (let TMP_22 \def (CHead e0 TMP_21 t) in (let TMP_23 +\def (Bind b0) in (let TMP_24 \def (CHead e0 TMP_23 t) in (eq C TMP_22 +TMP_24)))))) in (let TMP_30 \def (\lambda (c: C).(let TMP_26 \def (Bind b0) +in (let TMP_27 \def (CHead c TMP_26 u) in (let TMP_28 \def (Bind b0) in (let +TMP_29 \def (CHead c TMP_28 u) in (eq C TMP_27 TMP_29)))))) in (let TMP_35 +\def (\lambda (b1: B).(let TMP_31 \def (Bind b1) in (let TMP_32 \def (CHead e +TMP_31 u) in (let TMP_33 \def (Bind b1) in (let TMP_34 \def (CHead e TMP_33 +u) in (eq C TMP_32 TMP_34)))))) in (let TMP_36 \def (Bind b) in (let TMP_37 +\def (CHead e TMP_36 u) in (let TMP_38 \def (refl_equal C TMP_37) in (let +TMP_39 \def (eq_ind_r B b TMP_35 TMP_38 b0 H5) in (let TMP_40 \def (eq_ind_r +C e TMP_30 TMP_39 e0 H6) in (eq_ind_r T u TMP_25 TMP_40 u0 H4))))))))))) in +(let TMP_42 \def (TMP_41 H3) in (TMP_42 H2))))))))))))))))))))))))) in (let +TMP_52 \def (\lambda (e0: C).(\lambda (c: C).(\lambda (_: (clear e0 +c)).(\lambda (_: (((eq C e0 (CHead e (Bind b) u)) \to (eq C c e0)))).(\lambda +(f: F).(\lambda (u0: T).(\lambda (H3: (eq C (CHead e0 (Flat f) u0) (CHead e +(Bind b) u))).(let TMP_44 \def (Flat f) in (let TMP_45 \def (CHead e0 TMP_44 +u0) in (let TMP_46 \def (\lambda (ee: C).(match ee with [(CSort _) +\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _) +\Rightarrow False | (Flat _) \Rightarrow True])])) in (let TMP_47 \def (Bind +b) in (let TMP_48 \def (CHead e TMP_47 u) in (let H4 \def (eq_ind C TMP_45 +TMP_46 I TMP_48 H3) in (let TMP_49 \def (Flat f) in (let TMP_50 \def (CHead +e0 TMP_49 u0) in (let TMP_51 \def (eq C c TMP_50) in (False_ind TMP_51 +H4))))))))))))))))) in (clear_ind TMP_5 TMP_43 TMP_52 y x H0)))))) in +(insert_eq C TMP_2 TMP_3 TMP_4 TMP_53 H)))))))))). theorem clear_gen_flat: \forall (f: F).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear (CHead e (Flat f) u) x) \to (clear e x))))) \def \lambda (f: F).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: -(clear (CHead e (Flat f) u) x)).(insert_eq C (CHead e (Flat f) u) (\lambda -(c: C).(clear c x)) (\lambda (_: C).(clear e x)) (\lambda (y: C).(\lambda -(H0: (clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead -e (Flat f) u)) \to (clear e c0)))) (\lambda (b: B).(\lambda (e0: C).(\lambda -(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat f) -u))).(let H2 \def (eq_ind C (CHead e0 (Bind b) u0) (\lambda (ee: C).(match ee -in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead -_ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _) -\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e (Flat f) u) H1) -in (False_ind (clear e (CHead e0 (Bind b) u0)) H2)))))) (\lambda (e0: -C).(\lambda (c: C).(\lambda (H1: (clear e0 c)).(\lambda (H2: (((eq C e0 -(CHead e (Flat f) u)) \to (clear e c)))).(\lambda (f0: F).(\lambda (u0: -T).(\lambda (H3: (eq C (CHead e0 (Flat f0) u0) (CHead e (Flat f) u))).(let H4 -\def (f_equal C C (\lambda (e1: C).(match e1 in C return (\lambda (_: C).C) -with [(CSort _) \Rightarrow e0 | (CHead c0 _ _) \Rightarrow c0])) (CHead e0 -(Flat f0) u0) (CHead e (Flat f) u) H3) in ((let H5 \def (f_equal C F (\lambda -(e1: C).(match e1 in C return (\lambda (_: C).F) with [(CSort _) \Rightarrow -f0 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).F) with -[(Bind _) \Rightarrow f0 | (Flat f1) \Rightarrow f1])])) (CHead e0 (Flat f0) -u0) (CHead e (Flat f) u) H3) in ((let H6 \def (f_equal C T (\lambda (e1: -C).(match e1 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | -(CHead _ _ t) \Rightarrow t])) (CHead e0 (Flat f0) u0) (CHead e (Flat f) u) -H3) in (\lambda (_: (eq F f0 f)).(\lambda (H8: (eq C e0 e)).(let H9 \def -(eq_ind C e0 (\lambda (c0: C).((eq C c0 (CHead e (Flat f) u)) \to (clear e -c))) H2 e H8) in (let H10 \def (eq_ind C e0 (\lambda (c0: C).(clear c0 c)) H1 -e H8) in H10))))) H5)) H4))))))))) y x H0))) H))))). -(* COMMENTS -Initial nodes: 453 -END *) +(clear (CHead e (Flat f) u) x)).(let TMP_1 \def (Flat f) in (let TMP_2 \def +(CHead e TMP_1 u) in (let TMP_3 \def (\lambda (c: C).(clear c x)) in (let +TMP_4 \def (\lambda (_: C).(clear e x)) in (let TMP_35 \def (\lambda (y: +C).(\lambda (H0: (clear y x)).(let TMP_5 \def (\lambda (c: C).(\lambda (c0: +C).((eq C c (CHead e (Flat f) u)) \to (clear e c0)))) in (let TMP_14 \def +(\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(\lambda (H1: (eq C (CHead +e0 (Bind b) u0) (CHead e (Flat f) u))).(let TMP_6 \def (Bind b) in (let TMP_7 +\def (CHead e0 TMP_6 u0) in (let TMP_8 \def (\lambda (ee: C).(match ee with +[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind +_) \Rightarrow True | (Flat _) \Rightarrow False])])) in (let TMP_9 \def +(Flat f) in (let TMP_10 \def (CHead e TMP_9 u) in (let H2 \def (eq_ind C +TMP_7 TMP_8 I TMP_10 H1) in (let TMP_11 \def (Bind b) in (let TMP_12 \def +(CHead e0 TMP_11 u0) in (let TMP_13 \def (clear e TMP_12) in (False_ind +TMP_13 H2)))))))))))))) in (let TMP_34 \def (\lambda (e0: C).(\lambda (c: +C).(\lambda (H1: (clear e0 c)).(\lambda (H2: (((eq C e0 (CHead e (Flat f) u)) +\to (clear e c)))).(\lambda (f0: F).(\lambda (u0: T).(\lambda (H3: (eq C +(CHead e0 (Flat f0) u0) (CHead e (Flat f) u))).(let TMP_15 \def (\lambda (e1: +C).(match e1 with [(CSort _) \Rightarrow e0 | (CHead c0 _ _) \Rightarrow +c0])) in (let TMP_16 \def (Flat f0) in (let TMP_17 \def (CHead e0 TMP_16 u0) +in (let TMP_18 \def (Flat f) in (let TMP_19 \def (CHead e TMP_18 u) in (let +H4 \def (f_equal C C TMP_15 TMP_17 TMP_19 H3) in (let TMP_20 \def (\lambda +(e1: C).(match e1 with [(CSort _) \Rightarrow f0 | (CHead _ k _) \Rightarrow +(match k with [(Bind _) \Rightarrow f0 | (Flat f1) \Rightarrow f1])])) in +(let TMP_21 \def (Flat f0) in (let TMP_22 \def (CHead e0 TMP_21 u0) in (let +TMP_23 \def (Flat f) in (let TMP_24 \def (CHead e TMP_23 u) in (let H5 \def +(f_equal C F TMP_20 TMP_22 TMP_24 H3) in (let TMP_25 \def (\lambda (e1: +C).(match e1 with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) +in (let TMP_26 \def (Flat f0) in (let TMP_27 \def (CHead e0 TMP_26 u0) in +(let TMP_28 \def (Flat f) in (let TMP_29 \def (CHead e TMP_28 u) in (let H6 +\def (f_equal C T TMP_25 TMP_27 TMP_29 H3) in (let TMP_32 \def (\lambda (_: +(eq F f0 f)).(\lambda (H8: (eq C e0 e)).(let TMP_30 \def (\lambda (c0: +C).((eq C c0 (CHead e (Flat f) u)) \to (clear e c))) in (let H9 \def (eq_ind +C e0 TMP_30 H2 e H8) in (let TMP_31 \def (\lambda (c0: C).(clear c0 c)) in +(let H10 \def (eq_ind C e0 TMP_31 H1 e H8) in H10)))))) in (let TMP_33 \def +(TMP_32 H5) in (TMP_33 H4)))))))))))))))))))))))))))) in (clear_ind TMP_5 +TMP_14 TMP_34 y x H0)))))) in (insert_eq C TMP_2 TMP_3 TMP_4 TMP_35 +H)))))))))). theorem clear_gen_flat_r: \forall (f: F).(\forall (x: C).(\forall (e: C).(\forall (u: T).((clear x (CHead e (Flat f) u)) \to (\forall (P: Prop).P))))) \def \lambda (f: F).(\lambda (x: C).(\lambda (e: C).(\lambda (u: T).(\lambda (H: -(clear x (CHead e (Flat f) u))).(\lambda (P: Prop).(insert_eq C (CHead e -(Flat f) u) (\lambda (c: C).(clear x c)) (\lambda (_: C).P) (\lambda (y: -C).(\lambda (H0: (clear x y)).(clear_ind (\lambda (_: C).(\lambda (c0: -C).((eq C c0 (CHead e (Flat f) u)) \to P))) (\lambda (b: B).(\lambda (e0: -C).(\lambda (u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat -f) u))).(let H2 \def (eq_ind C (CHead e0 (Bind b) u0) (\lambda (ee: C).(match -ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | -(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with -[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e (Flat -f) u) H1) in (False_ind P H2)))))) (\lambda (e0: C).(\lambda (c: C).(\lambda -(H1: (clear e0 c)).(\lambda (H2: (((eq C c (CHead e (Flat f) u)) \to -P))).(\lambda (_: F).(\lambda (_: T).(\lambda (H3: (eq C c (CHead e (Flat f) -u))).(let H4 \def (eq_ind C c (\lambda (c0: C).((eq C c0 (CHead e (Flat f) -u)) \to P)) H2 (CHead e (Flat f) u) H3) in (let H5 \def (eq_ind C c (\lambda -(c0: C).(clear e0 c0)) H1 (CHead e (Flat f) u) H3) in (H4 (refl_equal C -(CHead e (Flat f) u)))))))))))) x y H0))) H)))))). -(* COMMENTS -Initial nodes: 303 -END *) +(clear x (CHead e (Flat f) u))).(\lambda (P: Prop).(let TMP_1 \def (Flat f) +in (let TMP_2 \def (CHead e TMP_1 u) in (let TMP_3 \def (\lambda (c: +C).(clear x c)) in (let TMP_4 \def (\lambda (_: C).P) in (let TMP_22 \def +(\lambda (y: C).(\lambda (H0: (clear x y)).(let TMP_5 \def (\lambda (_: +C).(\lambda (c0: C).((eq C c0 (CHead e (Flat f) u)) \to P))) in (let TMP_11 +\def (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(\lambda (H1: (eq C +(CHead e0 (Bind b) u0) (CHead e (Flat f) u))).(let TMP_6 \def (Bind b) in +(let TMP_7 \def (CHead e0 TMP_6 u0) in (let TMP_8 \def (\lambda (ee: +C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow +(match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) in +(let TMP_9 \def (Flat f) in (let TMP_10 \def (CHead e TMP_9 u) in (let H2 +\def (eq_ind C TMP_7 TMP_8 I TMP_10 H1) in (False_ind P H2))))))))))) in (let +TMP_21 \def (\lambda (e0: C).(\lambda (c: C).(\lambda (H1: (clear e0 +c)).(\lambda (H2: (((eq C c (CHead e (Flat f) u)) \to P))).(\lambda (_: +F).(\lambda (_: T).(\lambda (H3: (eq C c (CHead e (Flat f) u))).(let TMP_12 +\def (\lambda (c0: C).((eq C c0 (CHead e (Flat f) u)) \to P)) in (let TMP_13 +\def (Flat f) in (let TMP_14 \def (CHead e TMP_13 u) in (let H4 \def (eq_ind +C c TMP_12 H2 TMP_14 H3) in (let TMP_15 \def (\lambda (c0: C).(clear e0 c0)) +in (let TMP_16 \def (Flat f) in (let TMP_17 \def (CHead e TMP_16 u) in (let +H5 \def (eq_ind C c TMP_15 H1 TMP_17 H3) in (let TMP_18 \def (Flat f) in (let +TMP_19 \def (CHead e TMP_18 u) in (let TMP_20 \def (refl_equal C TMP_19) in +(H4 TMP_20))))))))))))))))))) in (clear_ind TMP_5 TMP_11 TMP_21 x y H0)))))) +in (insert_eq C TMP_2 TMP_3 TMP_4 TMP_22 H))))))))))). theorem clear_gen_all: \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (ex_3 B C T (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(eq C c2 (CHead e (Bind b) u)))))))) \def - \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (clear c1 c2)).(clear_ind -(\lambda (_: C).(\lambda (c0: C).(ex_3 B C T (\lambda (b: B).(\lambda (e: -C).(\lambda (u: T).(eq C c0 (CHead e (Bind b) u)))))))) (\lambda (b: -B).(\lambda (e: C).(\lambda (u: T).(ex_3_intro B C T (\lambda (b0: -B).(\lambda (e0: C).(\lambda (u0: T).(eq C (CHead e (Bind b) u) (CHead e0 -(Bind b0) u0))))) b e u (refl_equal C (CHead e (Bind b) u)))))) (\lambda (e: -C).(\lambda (c: C).(\lambda (H0: (clear e c)).(\lambda (H1: (ex_3 B C T + \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (clear c1 c2)).(let TMP_4 \def +(\lambda (_: C).(\lambda (c0: C).(let TMP_3 \def (\lambda (b: B).(\lambda (e: +C).(\lambda (u: T).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead e TMP_1 +u) in (eq C c0 TMP_2)))))) in (ex_3 B C T TMP_3)))) in (let TMP_13 \def +(\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(let TMP_9 \def (\lambda (b0: +B).(\lambda (e0: C).(\lambda (u0: T).(let TMP_5 \def (Bind b) in (let TMP_6 +\def (CHead e TMP_5 u) in (let TMP_7 \def (Bind b0) in (let TMP_8 \def (CHead +e0 TMP_7 u0) in (eq C TMP_6 TMP_8)))))))) in (let TMP_10 \def (Bind b) in +(let TMP_11 \def (CHead e TMP_10 u) in (let TMP_12 \def (refl_equal C TMP_11) +in (ex_3_intro B C T TMP_9 b e u TMP_12)))))))) in (let TMP_40 \def (\lambda +(e: C).(\lambda (c: C).(\lambda (H0: (clear e c)).(\lambda (H1: (ex_3 B C T (\lambda (b: B).(\lambda (e0: C).(\lambda (u: T).(eq C c (CHead e0 (Bind b) -u))))))).(\lambda (_: F).(\lambda (_: T).(let H2 \def H1 in (ex_3_ind B C T -(\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C c (CHead e0 (Bind b) -u0))))) (ex_3 B C T (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C c -(CHead e0 (Bind b) u0)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: -T).(\lambda (H3: (eq C c (CHead x1 (Bind x0) x2))).(let H4 \def (eq_ind C c -(\lambda (c0: C).(clear e c0)) H0 (CHead x1 (Bind x0) x2) H3) in (eq_ind_r C -(CHead x1 (Bind x0) x2) (\lambda (c0: C).(ex_3 B C T (\lambda (b: B).(\lambda -(e0: C).(\lambda (u0: T).(eq C c0 (CHead e0 (Bind b) u0))))))) (ex_3_intro B -C T (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(eq C (CHead x1 (Bind -x0) x2) (CHead e0 (Bind b) u0))))) x0 x1 x2 (refl_equal C (CHead x1 (Bind x0) -x2))) c H3)))))) H2)))))))) c1 c2 H))). -(* COMMENTS -Initial nodes: 381 -END *) +u))))))).(\lambda (_: F).(\lambda (_: T).(let H2 \def H1 in (let TMP_16 \def +(\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(let TMP_14 \def (Bind b) +in (let TMP_15 \def (CHead e0 TMP_14 u0) in (eq C c TMP_15)))))) in (let +TMP_19 \def (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(let TMP_17 +\def (Bind b) in (let TMP_18 \def (CHead e0 TMP_17 u0) in (eq C c +TMP_18)))))) in (let TMP_20 \def (ex_3 B C T TMP_19) in (let TMP_39 \def +(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H3: (eq C c +(CHead x1 (Bind x0) x2))).(let TMP_21 \def (\lambda (c0: C).(clear e c0)) in +(let TMP_22 \def (Bind x0) in (let TMP_23 \def (CHead x1 TMP_22 x2) in (let +H4 \def (eq_ind C c TMP_21 H0 TMP_23 H3) in (let TMP_24 \def (Bind x0) in +(let TMP_25 \def (CHead x1 TMP_24 x2) in (let TMP_29 \def (\lambda (c0: +C).(let TMP_28 \def (\lambda (b: B).(\lambda (e0: C).(\lambda (u0: T).(let +TMP_26 \def (Bind b) in (let TMP_27 \def (CHead e0 TMP_26 u0) in (eq C c0 +TMP_27)))))) in (ex_3 B C T TMP_28))) in (let TMP_34 \def (\lambda (b: +B).(\lambda (e0: C).(\lambda (u0: T).(let TMP_30 \def (Bind x0) in (let +TMP_31 \def (CHead x1 TMP_30 x2) in (let TMP_32 \def (Bind b) in (let TMP_33 +\def (CHead e0 TMP_32 u0) in (eq C TMP_31 TMP_33)))))))) in (let TMP_35 \def +(Bind x0) in (let TMP_36 \def (CHead x1 TMP_35 x2) in (let TMP_37 \def +(refl_equal C TMP_36) in (let TMP_38 \def (ex_3_intro B C T TMP_34 x0 x1 x2 +TMP_37) in (eq_ind_r C TMP_25 TMP_29 TMP_38 c H3))))))))))))))))) in +(ex_3_ind B C T TMP_16 TMP_20 TMP_39 H2)))))))))))) in (clear_ind TMP_4 +TMP_13 TMP_40 c1 c2 H)))))). + +theorem clear_mono: + \forall (c: C).(\forall (c1: C).((clear c c1) \to (\forall (c2: C).((clear c +c2) \to (eq C c1 c2))))) +\def + \lambda (c: C).(let TMP_1 \def (\lambda (c0: C).(\forall (c1: C).((clear c0 +c1) \to (\forall (c2: C).((clear c0 c2) \to (eq C c1 c2)))))) in (let TMP_3 +\def (\lambda (n: nat).(\lambda (c1: C).(\lambda (_: (clear (CSort n) +c1)).(\lambda (c2: C).(\lambda (H0: (clear (CSort n) c2)).(let TMP_2 \def (eq +C c1 c2) in (clear_gen_sort c2 n H0 TMP_2))))))) in (let TMP_23 \def (\lambda +(c0: C).(\lambda (H: ((\forall (c1: C).((clear c0 c1) \to (\forall (c2: +C).((clear c0 c2) \to (eq C c1 c2))))))).(\lambda (k: K).(\lambda (t: +T).(\lambda (c1: C).(\lambda (H0: (clear (CHead c0 k t) c1)).(\lambda (c2: +C).(\lambda (H1: (clear (CHead c0 k t) c2)).(let TMP_4 \def (\lambda (k0: +K).((clear (CHead c0 k0 t) c1) \to ((clear (CHead c0 k0 t) c2) \to (eq C c1 +c2)))) in (let TMP_19 \def (\lambda (b: B).(\lambda (H2: (clear (CHead c0 +(Bind b) t) c1)).(\lambda (H3: (clear (CHead c0 (Bind b) t) c2)).(let TMP_5 +\def (Bind b) in (let TMP_6 \def (CHead c0 TMP_5 t) in (let TMP_7 \def +(\lambda (c3: C).(eq C c1 c3)) in (let TMP_8 \def (Bind b) in (let TMP_9 \def +(CHead c0 TMP_8 t) in (let TMP_12 \def (\lambda (c3: C).(let TMP_10 \def +(Bind b) in (let TMP_11 \def (CHead c0 TMP_10 t) in (eq C c3 TMP_11)))) in +(let TMP_13 \def (Bind b) in (let TMP_14 \def (CHead c0 TMP_13 t) in (let +TMP_15 \def (refl_equal C TMP_14) in (let TMP_16 \def (clear_gen_bind b c0 c1 +t H2) in (let TMP_17 \def (eq_ind_r C TMP_9 TMP_12 TMP_15 c1 TMP_16) in (let +TMP_18 \def (clear_gen_bind b c0 c2 t H3) in (eq_ind_r C TMP_6 TMP_7 TMP_17 +c2 TMP_18)))))))))))))))) in (let TMP_22 \def (\lambda (f: F).(\lambda (H2: +(clear (CHead c0 (Flat f) t) c1)).(\lambda (H3: (clear (CHead c0 (Flat f) t) +c2)).(let TMP_20 \def (clear_gen_flat f c0 c1 t H2) in (let TMP_21 \def +(clear_gen_flat f c0 c2 t H3) in (H c1 TMP_20 c2 TMP_21)))))) in (K_ind TMP_4 +TMP_19 TMP_22 k H0 H1)))))))))))) in (C_ind TMP_1 TMP_3 TMP_23 c)))). + +theorem clear_cle: + \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (cle c2 c1))) +\def + \lambda (c1: C).(let TMP_3 \def (\lambda (c: C).(\forall (c2: C).((clear c +c2) \to (let TMP_1 \def (cweight c2) in (let TMP_2 \def (cweight c) in (le +TMP_1 TMP_2)))))) in (let TMP_6 \def (\lambda (n: nat).(\lambda (c2: +C).(\lambda (H: (clear (CSort n) c2)).(let TMP_4 \def (cweight c2) in (let +TMP_5 \def (le TMP_4 O) in (clear_gen_sort c2 n H TMP_5)))))) in (let TMP_31 +\def (\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (le +(cweight c2) (cweight c)))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: +C).(\lambda (H0: (clear (CHead c k t) c2)).(let TMP_11 \def (\lambda (k0: +K).((clear (CHead c k0 t) c2) \to (let TMP_7 \def (cweight c2) in (let TMP_8 +\def (cweight c) in (let TMP_9 \def (tweight t) in (let TMP_10 \def (plus +TMP_8 TMP_9) in (le TMP_7 TMP_10))))))) in (let TMP_24 \def (\lambda (b: +B).(\lambda (H1: (clear (CHead c (Bind b) t) c2)).(let TMP_12 \def (Bind b) +in (let TMP_13 \def (CHead c TMP_12 t) in (let TMP_18 \def (\lambda (c0: +C).(let TMP_14 \def (cweight c0) in (let TMP_15 \def (cweight c) in (let +TMP_16 \def (tweight t) in (let TMP_17 \def (plus TMP_15 TMP_16) in (le +TMP_14 TMP_17)))))) in (let TMP_19 \def (cweight c) in (let TMP_20 \def +(tweight t) in (let TMP_21 \def (plus TMP_19 TMP_20) in (let TMP_22 \def +(le_n TMP_21) in (let TMP_23 \def (clear_gen_bind b c c2 t H1) in (eq_ind_r C +TMP_13 TMP_18 TMP_22 c2 TMP_23))))))))))) in (let TMP_30 \def (\lambda (f: +F).(\lambda (H1: (clear (CHead c (Flat f) t) c2)).(let TMP_25 \def (cweight +c2) in (let TMP_26 \def (cweight c) in (let TMP_27 \def (tweight t) in (let +TMP_28 \def (clear_gen_flat f c c2 t H1) in (let TMP_29 \def (H c2 TMP_28) in +(le_plus_trans TMP_25 TMP_26 TMP_27 TMP_29)))))))) in (K_ind TMP_11 TMP_24 +TMP_30 k H0)))))))))) in (C_ind TMP_3 TMP_6 TMP_31 c1)))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma index 68e250d76..70f732a64 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma @@ -14,139 +14,133 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/clear/fwd.ma". +include "basic_1/clear/fwd.ma". theorem clear_clear: \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (clear c2 c2))) \def - \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to -(clear c2 c2)))) (\lambda (n: nat).(\lambda (c2: C).(\lambda (H: (clear -(CSort n) c2)).(clear_gen_sort c2 n H (clear c2 c2))))) (\lambda (c: + \lambda (c1: C).(let TMP_1 \def (\lambda (c: C).(\forall (c2: C).((clear c +c2) \to (clear c2 c2)))) in (let TMP_3 \def (\lambda (n: nat).(\lambda (c2: +C).(\lambda (H: (clear (CSort n) c2)).(let TMP_2 \def (clear c2 c2) in +(clear_gen_sort c2 n H TMP_2))))) in (let TMP_13 \def (\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (clear c2 c2))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (H0: (clear -(CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear (CHead c k0 t) c2) \to -(clear c2 c2))) (\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t) -c2)).(eq_ind_r C (CHead c (Bind b) t) (\lambda (c0: C).(clear c0 c0)) -(clear_bind b c t) c2 (clear_gen_bind b c c2 t H1)))) (\lambda (f: -F).(\lambda (H1: (clear (CHead c (Flat f) t) c2)).(H c2 (clear_gen_flat f c -c2 t H1)))) k H0))))))) c1). -(* COMMENTS -Initial nodes: 199 -END *) - -theorem clear_mono: - \forall (c: C).(\forall (c1: C).((clear c c1) \to (\forall (c2: C).((clear c -c2) \to (eq C c1 c2))))) -\def - \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (c1: C).((clear c0 c1) \to -(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2)))))) (\lambda (n: -nat).(\lambda (c1: C).(\lambda (_: (clear (CSort n) c1)).(\lambda (c2: -C).(\lambda (H0: (clear (CSort n) c2)).(clear_gen_sort c2 n H0 (eq C c1 -c2))))))) (\lambda (c0: C).(\lambda (H: ((\forall (c1: C).((clear c0 c1) \to -(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2))))))).(\lambda (k: -K).(\lambda (t: T).(\lambda (c1: C).(\lambda (H0: (clear (CHead c0 k t) -c1)).(\lambda (c2: C).(\lambda (H1: (clear (CHead c0 k t) c2)).(K_ind -(\lambda (k0: K).((clear (CHead c0 k0 t) c1) \to ((clear (CHead c0 k0 t) c2) -\to (eq C c1 c2)))) (\lambda (b: B).(\lambda (H2: (clear (CHead c0 (Bind b) -t) c1)).(\lambda (H3: (clear (CHead c0 (Bind b) t) c2)).(eq_ind_r C (CHead c0 -(Bind b) t) (\lambda (c3: C).(eq C c1 c3)) (eq_ind_r C (CHead c0 (Bind b) t) -(\lambda (c3: C).(eq C c3 (CHead c0 (Bind b) t))) (refl_equal C (CHead c0 -(Bind b) t)) c1 (clear_gen_bind b c0 c1 t H2)) c2 (clear_gen_bind b c0 c2 t -H3))))) (\lambda (f: F).(\lambda (H2: (clear (CHead c0 (Flat f) t) -c1)).(\lambda (H3: (clear (CHead c0 (Flat f) t) c2)).(H c1 (clear_gen_flat f -c0 c1 t H2) c2 (clear_gen_flat f c0 c2 t H3))))) k H0 H1))))))))) c). -(* COMMENTS -Initial nodes: 357 -END *) +(CHead c k t) c2)).(let TMP_4 \def (\lambda (k0: K).((clear (CHead c k0 t) +c2) \to (clear c2 c2))) in (let TMP_10 \def (\lambda (b: B).(\lambda (H1: +(clear (CHead c (Bind b) t) c2)).(let TMP_5 \def (Bind b) in (let TMP_6 \def +(CHead c TMP_5 t) in (let TMP_7 \def (\lambda (c0: C).(clear c0 c0)) in (let +TMP_8 \def (clear_bind b c t) in (let TMP_9 \def (clear_gen_bind b c c2 t H1) +in (eq_ind_r C TMP_6 TMP_7 TMP_8 c2 TMP_9)))))))) in (let TMP_12 \def +(\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t) c2)).(let TMP_11 +\def (clear_gen_flat f c c2 t H1) in (H c2 TMP_11)))) in (K_ind TMP_4 TMP_10 +TMP_12 k H0)))))))))) in (C_ind TMP_1 TMP_3 TMP_13 c1)))). theorem clear_trans: \forall (c1: C).(\forall (c: C).((clear c1 c) \to (\forall (c2: C).((clear c c2) \to (clear c1 c2))))) \def - \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c0: C).((clear c c0) \to -(\forall (c2: C).((clear c0 c2) \to (clear c c2)))))) (\lambda (n: -nat).(\lambda (c: C).(\lambda (H: (clear (CSort n) c)).(\lambda (c2: -C).(\lambda (_: (clear c c2)).(clear_gen_sort c n H (clear (CSort n) -c2))))))) (\lambda (c: C).(\lambda (H: ((\forall (c0: C).((clear c c0) \to -(\forall (c2: C).((clear c0 c2) \to (clear c c2))))))).(\lambda (k: + \lambda (c1: C).(let TMP_1 \def (\lambda (c: C).(\forall (c0: C).((clear c +c0) \to (\forall (c2: C).((clear c0 c2) \to (clear c c2)))))) in (let TMP_4 +\def (\lambda (n: nat).(\lambda (c: C).(\lambda (H: (clear (CSort n) +c)).(\lambda (c2: C).(\lambda (_: (clear c c2)).(let TMP_2 \def (CSort n) in +(let TMP_3 \def (clear TMP_2 c2) in (clear_gen_sort c n H TMP_3)))))))) in +(let TMP_22 \def (\lambda (c: C).(\lambda (H: ((\forall (c0: C).((clear c c0) +\to (\forall (c2: C).((clear c0 c2) \to (clear c c2))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c0: C).(\lambda (H0: (clear (CHead c k t) -c0)).(\lambda (c2: C).(\lambda (H1: (clear c0 c2)).(K_ind (\lambda (k0: -K).((clear (CHead c k0 t) c0) \to (clear (CHead c k0 t) c2))) (\lambda (b: -B).(\lambda (H2: (clear (CHead c (Bind b) t) c0)).(let H3 \def (eq_ind C c0 -(\lambda (c3: C).(clear c3 c2)) H1 (CHead c (Bind b) t) (clear_gen_bind b c -c0 t H2)) in (eq_ind_r C (CHead c (Bind b) t) (\lambda (c3: C).(clear (CHead -c (Bind b) t) c3)) (clear_bind b c t) c2 (clear_gen_bind b c c2 t H3))))) -(\lambda (f: F).(\lambda (H2: (clear (CHead c (Flat f) t) c0)).(clear_flat c -c2 (H c0 (clear_gen_flat f c c0 t H2) c2 H1) f t))) k H0))))))))) c1). -(* COMMENTS -Initial nodes: 299 -END *) +c0)).(\lambda (c2: C).(\lambda (H1: (clear c0 c2)).(let TMP_6 \def (\lambda +(k0: K).((clear (CHead c k0 t) c0) \to (let TMP_5 \def (CHead c k0 t) in +(clear TMP_5 c2)))) in (let TMP_18 \def (\lambda (b: B).(\lambda (H2: (clear +(CHead c (Bind b) t) c0)).(let TMP_7 \def (\lambda (c3: C).(clear c3 c2)) in +(let TMP_8 \def (Bind b) in (let TMP_9 \def (CHead c TMP_8 t) in (let TMP_10 +\def (clear_gen_bind b c c0 t H2) in (let H3 \def (eq_ind C c0 TMP_7 H1 TMP_9 +TMP_10) in (let TMP_11 \def (Bind b) in (let TMP_12 \def (CHead c TMP_11 t) +in (let TMP_15 \def (\lambda (c3: C).(let TMP_13 \def (Bind b) in (let TMP_14 +\def (CHead c TMP_13 t) in (clear TMP_14 c3)))) in (let TMP_16 \def +(clear_bind b c t) in (let TMP_17 \def (clear_gen_bind b c c2 t H3) in +(eq_ind_r C TMP_12 TMP_15 TMP_16 c2 TMP_17))))))))))))) in (let TMP_21 \def +(\lambda (f: F).(\lambda (H2: (clear (CHead c (Flat f) t) c0)).(let TMP_19 +\def (clear_gen_flat f c c0 t H2) in (let TMP_20 \def (H c0 TMP_19 c2 H1) in +(clear_flat c c2 TMP_20 f t))))) in (K_ind TMP_6 TMP_18 TMP_21 k +H0)))))))))))) in (C_ind TMP_1 TMP_4 TMP_22 c1)))). theorem clear_ctail: \forall (b: B).(\forall (c1: C).(\forall (c2: C).(\forall (u2: T).((clear c1 (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1: T).(clear (CTail k u1 c1) (CHead (CTail k u1 c2) (Bind b) u2)))))))) \def - \lambda (b: B).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: + \lambda (b: B).(\lambda (c1: C).(let TMP_5 \def (\lambda (c: C).(\forall +(c2: C).(\forall (u2: T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k: +K).(\forall (u1: T).(let TMP_1 \def (CTail k u1 c) in (let TMP_2 \def (CTail +k u1 c2) in (let TMP_3 \def (Bind b) in (let TMP_4 \def (CHead TMP_2 TMP_3 +u2) in (clear TMP_1 TMP_4))))))))))) in (let TMP_34 \def (\lambda (n: +nat).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H: (clear (CSort n) (CHead +c2 (Bind b) u2))).(\lambda (k: K).(\lambda (u1: T).(let TMP_11 \def (\lambda +(k0: K).(let TMP_6 \def (CSort n) in (let TMP_7 \def (CHead TMP_6 k0 u1) in +(let TMP_8 \def (CTail k0 u1 c2) in (let TMP_9 \def (Bind b) in (let TMP_10 +\def (CHead TMP_8 TMP_9 u2) in (clear TMP_7 TMP_10))))))) in (let TMP_22 \def +(\lambda (b0: B).(let TMP_12 \def (Bind b) in (let TMP_13 \def (CHead c2 +TMP_12 u2) in (let TMP_14 \def (CSort n) in (let TMP_15 \def (Bind b0) in +(let TMP_16 \def (CHead TMP_14 TMP_15 u1) in (let TMP_17 \def (Bind b0) in +(let TMP_18 \def (CTail TMP_17 u1 c2) in (let TMP_19 \def (Bind b) in (let +TMP_20 \def (CHead TMP_18 TMP_19 u2) in (let TMP_21 \def (clear TMP_16 +TMP_20) in (clear_gen_sort TMP_13 n H TMP_21)))))))))))) in (let TMP_33 \def +(\lambda (f: F).(let TMP_23 \def (Bind b) in (let TMP_24 \def (CHead c2 +TMP_23 u2) in (let TMP_25 \def (CSort n) in (let TMP_26 \def (Flat f) in (let +TMP_27 \def (CHead TMP_25 TMP_26 u1) in (let TMP_28 \def (Flat f) in (let +TMP_29 \def (CTail TMP_28 u1 c2) in (let TMP_30 \def (Bind b) in (let TMP_31 +\def (CHead TMP_29 TMP_30 u2) in (let TMP_32 \def (clear TMP_27 TMP_31) in +(clear_gen_sort TMP_24 n H TMP_32)))))))))))) in (K_ind TMP_11 TMP_22 TMP_33 +k)))))))))) in (let TMP_102 \def (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall (u2: T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1: T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b) -u2)))))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H: -(clear (CSort n) (CHead c2 (Bind b) u2))).(\lambda (k: K).(\lambda (u1: -T).(K_ind (\lambda (k0: K).(clear (CHead (CSort n) k0 u1) (CHead (CTail k0 u1 -c2) (Bind b) u2))) (\lambda (b0: B).(clear_gen_sort (CHead c2 (Bind b) u2) n -H (clear (CHead (CSort n) (Bind b0) u1) (CHead (CTail (Bind b0) u1 c2) (Bind -b) u2)))) (\lambda (f: F).(clear_gen_sort (CHead c2 (Bind b) u2) n H (clear -(CHead (CSort n) (Flat f) u1) (CHead (CTail (Flat f) u1 c2) (Bind b) u2)))) -k))))))) (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall (u2: -T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1: -T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b) u2))))))))).(\lambda -(k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H0: (clear -(CHead c k t) (CHead c2 (Bind b) u2))).(\lambda (k0: K).(\lambda (u1: -T).(K_ind (\lambda (k1: K).((clear (CHead c k1 t) (CHead c2 (Bind b) u2)) \to -(clear (CHead (CTail k0 u1 c) k1 t) (CHead (CTail k0 u1 c2) (Bind b) u2)))) -(\lambda (b0: B).(\lambda (H1: (clear (CHead c (Bind b0) t) (CHead c2 (Bind -b) u2))).(let H2 \def (f_equal C C (\lambda (e: C).(match e in C return -(\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) -\Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t) -(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in ((let H3 \def (f_equal -C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) -\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 in K return (\lambda (_: -K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2 -(Bind b) u2) (CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) -u2) t H1)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e in C return -(\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t0) -\Rightarrow t0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t) -(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in (\lambda (H5: (eq B b -b0)).(\lambda (H6: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: T).(clear (CHead -(CTail k0 u1 c) (Bind b0) t) (CHead (CTail k0 u1 c2) (Bind b) t0))) (eq_ind_r -C c (\lambda (c0: C).(clear (CHead (CTail k0 u1 c) (Bind b0) t) (CHead (CTail -k0 u1 c0) (Bind b) t))) (eq_ind B b (\lambda (b1: B).(clear (CHead (CTail k0 -u1 c) (Bind b1) t) (CHead (CTail k0 u1 c) (Bind b) t))) (clear_bind b (CTail -k0 u1 c) t) b0 H5) c2 H6) u2 H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1: -(clear (CHead c (Flat f) t) (CHead c2 (Bind b) u2))).(clear_flat (CTail k0 u1 -c) (CHead (CTail k0 u1 c2) (Bind b) u2) (H c2 u2 (clear_gen_flat f c (CHead -c2 (Bind b) u2) t H1) k0 u1) f t))) k H0)))))))))) c1)). -(* COMMENTS -Initial nodes: 819 -END *) - -theorem clear_cle: - \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (cle c2 c1))) -\def - \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to -(le (cweight c2) (cweight c))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda -(H: (clear (CSort n) c2)).(clear_gen_sort c2 n H (le (cweight c2) O))))) -(\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (le (cweight -c2) (cweight c)))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: -C).(\lambda (H0: (clear (CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear -(CHead c k0 t) c2) \to (le (cweight c2) (plus (cweight c) (tweight t))))) -(\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t) c2)).(eq_ind_r C -(CHead c (Bind b) t) (\lambda (c0: C).(le (cweight c0) (plus (cweight c) -(tweight t)))) (le_n (plus (cweight c) (tweight t))) c2 (clear_gen_bind b c -c2 t H1)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t) -c2)).(le_plus_trans (cweight c2) (cweight c) (tweight t) (H c2 -(clear_gen_flat f c c2 t H1))))) k H0))))))) c1). -(* COMMENTS -Initial nodes: 247 -END *) +u2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (u2: +T).(\lambda (H0: (clear (CHead c k t) (CHead c2 (Bind b) u2))).(\lambda (k0: +K).(\lambda (u1: T).(let TMP_40 \def (\lambda (k1: K).((clear (CHead c k1 t) +(CHead c2 (Bind b) u2)) \to (let TMP_35 \def (CTail k0 u1 c) in (let TMP_36 +\def (CHead TMP_35 k1 t) in (let TMP_37 \def (CTail k0 u1 c2) in (let TMP_38 +\def (Bind b) in (let TMP_39 \def (CHead TMP_37 TMP_38 u2) in (clear TMP_36 +TMP_39)))))))) in (let TMP_92 \def (\lambda (b0: B).(\lambda (H1: (clear +(CHead c (Bind b0) t) (CHead c2 (Bind b) u2))).(let TMP_41 \def (\lambda (e: +C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) +in (let TMP_42 \def (Bind b) in (let TMP_43 \def (CHead c2 TMP_42 u2) in (let +TMP_44 \def (Bind b0) in (let TMP_45 \def (CHead c TMP_44 t) in (let TMP_46 +\def (Bind b) in (let TMP_47 \def (CHead c2 TMP_46 u2) in (let TMP_48 \def +(clear_gen_bind b0 c TMP_47 t H1) in (let H2 \def (f_equal C C TMP_41 TMP_43 +TMP_45 TMP_48) in (let TMP_49 \def (\lambda (e: C).(match e with [(CSort _) +\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 with [(Bind b1) +\Rightarrow b1 | (Flat _) \Rightarrow b])])) in (let TMP_50 \def (Bind b) in +(let TMP_51 \def (CHead c2 TMP_50 u2) in (let TMP_52 \def (Bind b0) in (let +TMP_53 \def (CHead c TMP_52 t) in (let TMP_54 \def (Bind b) in (let TMP_55 +\def (CHead c2 TMP_54 u2) in (let TMP_56 \def (clear_gen_bind b0 c TMP_55 t +H1) in (let H3 \def (f_equal C B TMP_49 TMP_51 TMP_53 TMP_56) in (let TMP_57 +\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | (CHead _ _ t0) +\Rightarrow t0])) in (let TMP_58 \def (Bind b) in (let TMP_59 \def (CHead c2 +TMP_58 u2) in (let TMP_60 \def (Bind b0) in (let TMP_61 \def (CHead c TMP_60 +t) in (let TMP_62 \def (Bind b) in (let TMP_63 \def (CHead c2 TMP_62 u2) in +(let TMP_64 \def (clear_gen_bind b0 c TMP_63 t H1) in (let H4 \def (f_equal C +T TMP_57 TMP_59 TMP_61 TMP_64) in (let TMP_90 \def (\lambda (H5: (eq B b +b0)).(\lambda (H6: (eq C c2 c)).(let TMP_71 \def (\lambda (t0: T).(let TMP_65 +\def (CTail k0 u1 c) in (let TMP_66 \def (Bind b0) in (let TMP_67 \def (CHead +TMP_65 TMP_66 t) in (let TMP_68 \def (CTail k0 u1 c2) in (let TMP_69 \def +(Bind b) in (let TMP_70 \def (CHead TMP_68 TMP_69 t0) in (clear TMP_67 +TMP_70)))))))) in (let TMP_78 \def (\lambda (c0: C).(let TMP_72 \def (CTail +k0 u1 c) in (let TMP_73 \def (Bind b0) in (let TMP_74 \def (CHead TMP_72 +TMP_73 t) in (let TMP_75 \def (CTail k0 u1 c0) in (let TMP_76 \def (Bind b) +in (let TMP_77 \def (CHead TMP_75 TMP_76 t) in (clear TMP_74 TMP_77)))))))) +in (let TMP_85 \def (\lambda (b1: B).(let TMP_79 \def (CTail k0 u1 c) in (let +TMP_80 \def (Bind b1) in (let TMP_81 \def (CHead TMP_79 TMP_80 t) in (let +TMP_82 \def (CTail k0 u1 c) in (let TMP_83 \def (Bind b) in (let TMP_84 \def +(CHead TMP_82 TMP_83 t) in (clear TMP_81 TMP_84)))))))) in (let TMP_86 \def +(CTail k0 u1 c) in (let TMP_87 \def (clear_bind b TMP_86 t) in (let TMP_88 +\def (eq_ind B b TMP_85 TMP_87 b0 H5) in (let TMP_89 \def (eq_ind_r C c +TMP_78 TMP_88 c2 H6) in (eq_ind_r T t TMP_71 TMP_89 u2 H4)))))))))) in (let +TMP_91 \def (TMP_90 H3) in (TMP_91 H2)))))))))))))))))))))))))))))))) in (let +TMP_101 \def (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t) (CHead +c2 (Bind b) u2))).(let TMP_93 \def (CTail k0 u1 c) in (let TMP_94 \def (CTail +k0 u1 c2) in (let TMP_95 \def (Bind b) in (let TMP_96 \def (CHead TMP_94 +TMP_95 u2) in (let TMP_97 \def (Bind b) in (let TMP_98 \def (CHead c2 TMP_97 +u2) in (let TMP_99 \def (clear_gen_flat f c TMP_98 t H1) in (let TMP_100 \def +(H c2 u2 TMP_99 k0 u1) in (clear_flat TMP_93 TMP_96 TMP_100 f t))))))))))) in +(K_ind TMP_40 TMP_92 TMP_101 k H0))))))))))))) in (C_ind TMP_5 TMP_34 TMP_102 +c1))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/clear.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/clear.ma index de0a85bd3..ab74ba390 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/clear.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/clear.ma @@ -14,42 +14,50 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/props.ma". +include "basic_1/getl/props.ma". -include "Basic-1/clear/drop.ma". +include "basic_1/clear/drop.ma". theorem clear_getl_trans: \forall (i: nat).(\forall (c2: C).(\forall (c3: C).((getl i c2 c3) \to (\forall (c1: C).((clear c1 c2) \to (getl i c1 c3)))))) \def - \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c2: C).(\forall (c3: -C).((getl n c2 c3) \to (\forall (c1: C).((clear c1 c2) \to (getl n c1 -c3))))))) (\lambda (c2: C).(\lambda (c3: C).(\lambda (H: (getl O c2 -c3)).(\lambda (c1: C).(\lambda (H0: (clear c1 c2)).(getl_intro O c1 c3 c1 -(drop_refl c1) (clear_trans c1 c2 H0 c3 (getl_gen_O c2 c3 H)))))))) (\lambda -(n: nat).(\lambda (_: ((\forall (c2: C).(\forall (c3: C).((getl n c2 c3) \to -(\forall (c1: C).((clear c1 c2) \to (getl n c1 c3)))))))).(\lambda (c2: -C).(C_ind (\lambda (c: C).(\forall (c3: C).((getl (S n) c c3) \to (\forall -(c1: C).((clear c1 c) \to (getl (S n) c1 c3)))))) (\lambda (n0: nat).(\lambda -(c3: C).(\lambda (H0: (getl (S n) (CSort n0) c3)).(\lambda (c1: C).(\lambda -(_: (clear c1 (CSort n0))).(getl_gen_sort n0 (S n) c3 H0 (getl (S n) c1 -c3))))))) (\lambda (c: C).(\lambda (_: ((\forall (c3: C).((getl (S n) c c3) -\to (\forall (c1: C).((clear c1 c) \to (getl (S n) c1 c3))))))).(\lambda (k: -K).(\lambda (t: T).(\lambda (c3: C).(\lambda (H1: (getl (S n) (CHead c k t) -c3)).(\lambda (c1: C).(\lambda (H2: (clear c1 (CHead c k t))).(K_ind (\lambda + \lambda (i: nat).(let TMP_1 \def (\lambda (n: nat).(\forall (c2: C).(\forall +(c3: C).((getl n c2 c3) \to (\forall (c1: C).((clear c1 c2) \to (getl n c1 +c3))))))) in (let TMP_5 \def (\lambda (c2: C).(\lambda (c3: C).(\lambda (H: +(getl O c2 c3)).(\lambda (c1: C).(\lambda (H0: (clear c1 c2)).(let TMP_2 \def +(drop_refl c1) in (let TMP_3 \def (getl_gen_O c2 c3 H) in (let TMP_4 \def +(clear_trans c1 c2 H0 c3 TMP_3) in (getl_intro O c1 c3 c1 TMP_2 +TMP_4))))))))) in (let TMP_30 \def (\lambda (n: nat).(\lambda (_: ((\forall +(c2: C).(\forall (c3: C).((getl n c2 c3) \to (\forall (c1: C).((clear c1 c2) +\to (getl n c1 c3)))))))).(\lambda (c2: C).(let TMP_7 \def (\lambda (c: +C).(\forall (c3: C).((getl (S n) c c3) \to (\forall (c1: C).((clear c1 c) \to +(let TMP_6 \def (S n) in (getl TMP_6 c1 c3))))))) in (let TMP_11 \def +(\lambda (n0: nat).(\lambda (c3: C).(\lambda (H0: (getl (S n) (CSort n0) +c3)).(\lambda (c1: C).(\lambda (_: (clear c1 (CSort n0))).(let TMP_8 \def (S +n) in (let TMP_9 \def (S n) in (let TMP_10 \def (getl TMP_9 c1 c3) in +(getl_gen_sort n0 TMP_8 c3 H0 TMP_10))))))))) in (let TMP_29 \def (\lambda +(c: C).(\lambda (_: ((\forall (c3: C).((getl (S n) c c3) \to (\forall (c1: +C).((clear c1 c) \to (getl (S n) c1 c3))))))).(\lambda (k: K).(\lambda (t: +T).(\lambda (c3: C).(\lambda (H1: (getl (S n) (CHead c k t) c3)).(\lambda +(c1: C).(\lambda (H2: (clear c1 (CHead c k t))).(let TMP_13 \def (\lambda (k0: K).((getl (S n) (CHead c k0 t) c3) \to ((clear c1 (CHead c k0 t)) \to -(getl (S n) c1 c3)))) (\lambda (b: B).(\lambda (H3: (getl (S n) (CHead c -(Bind b) t) c3)).(\lambda (H4: (clear c1 (CHead c (Bind b) t))).(let H5 \def -(getl_gen_all c c3 (r (Bind b) n) (getl_gen_S (Bind b) c c3 t n H3)) in -(ex2_ind C (\lambda (e: C).(drop n O c e)) (\lambda (e: C).(clear e c3)) -(getl (S n) c1 c3) (\lambda (x: C).(\lambda (H6: (drop n O c x)).(\lambda -(H7: (clear x c3)).(getl_intro (S n) c1 c3 x (drop_clear_O b c1 c t H4 x n -H6) H7)))) H5))))) (\lambda (f: F).(\lambda (_: (getl (S n) (CHead c (Flat f) -t) c3)).(\lambda (H4: (clear c1 (CHead c (Flat f) t))).(clear_gen_flat_r f c1 -c t H4 (getl (S n) c1 c3))))) k H1 H2))))))))) c2)))) i). -(* COMMENTS -Initial nodes: 525 -END *) +(let TMP_12 \def (S n) in (getl TMP_12 c1 c3))))) in (let TMP_25 \def +(\lambda (b: B).(\lambda (H3: (getl (S n) (CHead c (Bind b) t) c3)).(\lambda +(H4: (clear c1 (CHead c (Bind b) t))).(let TMP_14 \def (Bind b) in (let +TMP_15 \def (r TMP_14 n) in (let TMP_16 \def (Bind b) in (let TMP_17 \def +(getl_gen_S TMP_16 c c3 t n H3) in (let H5 \def (getl_gen_all c c3 TMP_15 +TMP_17) in (let TMP_18 \def (\lambda (e: C).(drop n O c e)) in (let TMP_19 +\def (\lambda (e: C).(clear e c3)) in (let TMP_20 \def (S n) in (let TMP_21 +\def (getl TMP_20 c1 c3) in (let TMP_24 \def (\lambda (x: C).(\lambda (H6: +(drop n O c x)).(\lambda (H7: (clear x c3)).(let TMP_22 \def (S n) in (let +TMP_23 \def (drop_clear_O b c1 c t H4 x n H6) in (getl_intro TMP_22 c1 c3 x +TMP_23 H7)))))) in (ex2_ind C TMP_18 TMP_19 TMP_21 TMP_24 H5)))))))))))))) in +(let TMP_28 \def (\lambda (f: F).(\lambda (_: (getl (S n) (CHead c (Flat f) +t) c3)).(\lambda (H4: (clear c1 (CHead c (Flat f) t))).(let TMP_26 \def (S n) +in (let TMP_27 \def (getl TMP_26 c1 c3) in (clear_gen_flat_r f c1 c t H4 +TMP_27)))))) in (K_ind TMP_13 TMP_25 TMP_28 k H1 H2)))))))))))) in (C_ind +TMP_7 TMP_11 TMP_29 c2))))))) in (nat_ind TMP_1 TMP_5 TMP_30 i)))). theorem getl_clear_trans: \forall (i: nat).(\forall (c1: C).(\forall (c2: C).((getl i c1 c2) \to @@ -57,97 +65,129 @@ theorem getl_clear_trans: \def \lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (getl i c1 c2)).(\lambda (c3: C).(\lambda (H0: (clear c2 c3)).(let H1 \def (getl_gen_all -c1 c2 i H) in (ex2_ind C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: -C).(clear e c2)) (getl i c1 c3) (\lambda (x: C).(\lambda (H2: (drop i O c1 -x)).(\lambda (H3: (clear x c2)).(let H4 \def (clear_gen_all x c2 H3) in -(ex_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(eq C c2 -(CHead e (Bind b) u))))) (getl i c1 c3) (\lambda (x0: B).(\lambda (x1: -C).(\lambda (x2: T).(\lambda (H5: (eq C c2 (CHead x1 (Bind x0) x2))).(let H6 -\def (eq_ind C c2 (\lambda (c: C).(clear x c)) H3 (CHead x1 (Bind x0) x2) H5) -in (let H7 \def (eq_ind C c2 (\lambda (c: C).(clear c c3)) H0 (CHead x1 (Bind -x0) x2) H5) in (eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c: C).(getl i c1 -c)) (getl_intro i c1 (CHead x1 (Bind x0) x2) x H2 H6) c3 (clear_gen_bind x0 -x1 c3 x2 H7)))))))) H4))))) H1))))))). -(* COMMENTS -Initial nodes: 269 -END *) +c1 c2 i H) in (let TMP_1 \def (\lambda (e: C).(drop i O c1 e)) in (let TMP_2 +\def (\lambda (e: C).(clear e c2)) in (let TMP_3 \def (getl i c1 c3) in (let +TMP_22 \def (\lambda (x: C).(\lambda (H2: (drop i O c1 x)).(\lambda (H3: +(clear x c2)).(let H4 \def (clear_gen_all x c2 H3) in (let TMP_6 \def +(\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(let TMP_4 \def (Bind b) in +(let TMP_5 \def (CHead e TMP_4 u) in (eq C c2 TMP_5)))))) in (let TMP_7 \def +(getl i c1 c3) in (let TMP_21 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda +(x2: T).(\lambda (H5: (eq C c2 (CHead x1 (Bind x0) x2))).(let TMP_8 \def +(\lambda (c: C).(clear x c)) in (let TMP_9 \def (Bind x0) in (let TMP_10 \def +(CHead x1 TMP_9 x2) in (let H6 \def (eq_ind C c2 TMP_8 H3 TMP_10 H5) in (let +TMP_11 \def (\lambda (c: C).(clear c c3)) in (let TMP_12 \def (Bind x0) in +(let TMP_13 \def (CHead x1 TMP_12 x2) in (let H7 \def (eq_ind C c2 TMP_11 H0 +TMP_13 H5) in (let TMP_14 \def (Bind x0) in (let TMP_15 \def (CHead x1 TMP_14 +x2) in (let TMP_16 \def (\lambda (c: C).(getl i c1 c)) in (let TMP_17 \def +(Bind x0) in (let TMP_18 \def (CHead x1 TMP_17 x2) in (let TMP_19 \def +(getl_intro i c1 TMP_18 x H2 H6) in (let TMP_20 \def (clear_gen_bind x0 x1 c3 +x2 H7) in (eq_ind_r C TMP_15 TMP_16 TMP_19 c3 TMP_20)))))))))))))))))))) in +(ex_3_ind B C T TMP_6 TMP_7 TMP_21 H4)))))))) in (ex2_ind C TMP_1 TMP_2 TMP_3 +TMP_22 H1))))))))))). theorem getl_clear_bind: \forall (b: B).(\forall (c: C).(\forall (e1: C).(\forall (v: T).((clear c (CHead e1 (Bind b) v)) \to (\forall (e2: C).(\forall (n: nat).((getl n e1 e2) \to (getl (S n) c e2)))))))) \def - \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e1: -C).(\forall (v: T).((clear c0 (CHead e1 (Bind b) v)) \to (\forall (e2: -C).(\forall (n: nat).((getl n e1 e2) \to (getl (S n) c0 e2)))))))) (\lambda -(n: nat).(\lambda (e1: C).(\lambda (v: T).(\lambda (H: (clear (CSort n) -(CHead e1 (Bind b) v))).(\lambda (e2: C).(\lambda (n0: nat).(\lambda (_: -(getl n0 e1 e2)).(clear_gen_sort (CHead e1 (Bind b) v) n H (getl (S n0) -(CSort n) e2))))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e1: -C).(\forall (v: T).((clear c0 (CHead e1 (Bind b) v)) \to (\forall (e2: -C).(\forall (n: nat).((getl n e1 e2) \to (getl (S n) c0 e2))))))))).(\lambda -(k: K).(\lambda (t: T).(\lambda (e1: C).(\lambda (v: T).(\lambda (H0: (clear -(CHead c0 k t) (CHead e1 (Bind b) v))).(\lambda (e2: C).(\lambda (n: -nat).(\lambda (H1: (getl n e1 e2)).(K_ind (\lambda (k0: K).((clear (CHead c0 -k0 t) (CHead e1 (Bind b) v)) \to (getl (S n) (CHead c0 k0 t) e2))) (\lambda -(b0: B).(\lambda (H2: (clear (CHead c0 (Bind b0) t) (CHead e1 (Bind b) -v))).(let H3 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda -(_: C).C) with [(CSort _) \Rightarrow e1 | (CHead c1 _ _) \Rightarrow c1])) -(CHead e1 (Bind b) v) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 -(Bind b) v) t H2)) in ((let H4 \def (f_equal C B (\lambda (e: C).(match e in -C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k0 _) -\Rightarrow (match k0 in K return (\lambda (_: K).B) with [(Bind b1) -\Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e1 (Bind b) v) (CHead c0 -(Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 (Bind b) v) t H2)) in ((let H5 -\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) -with [(CSort _) \Rightarrow v | (CHead _ _ t0) \Rightarrow t0])) (CHead e1 -(Bind b) v) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 (Bind b) -v) t H2)) in (\lambda (H6: (eq B b b0)).(\lambda (H7: (eq C e1 c0)).(let H8 -\def (eq_ind C e1 (\lambda (c1: C).(getl n c1 e2)) H1 c0 H7) in (eq_ind B b -(\lambda (b1: B).(getl (S n) (CHead c0 (Bind b1) t) e2)) (getl_head (Bind b) -n c0 e2 H8 t) b0 H6))))) H4)) H3)))) (\lambda (f: F).(\lambda (H2: (clear -(CHead c0 (Flat f) t) (CHead e1 (Bind b) v))).(getl_flat c0 e2 (S n) (H e1 v -(clear_gen_flat f c0 (CHead e1 (Bind b) v) t H2) e2 n H1) f t))) k -H0))))))))))) c)). -(* COMMENTS -Initial nodes: 599 -END *) + \lambda (b: B).(\lambda (c: C).(let TMP_2 \def (\lambda (c0: C).(\forall +(e1: C).(\forall (v: T).((clear c0 (CHead e1 (Bind b) v)) \to (\forall (e2: +C).(\forall (n: nat).((getl n e1 e2) \to (let TMP_1 \def (S n) in (getl TMP_1 +c0 e2))))))))) in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda +(v: T).(\lambda (H: (clear (CSort n) (CHead e1 (Bind b) v))).(\lambda (e2: +C).(\lambda (n0: nat).(\lambda (_: (getl n0 e1 e2)).(let TMP_3 \def (Bind b) +in (let TMP_4 \def (CHead e1 TMP_3 v) in (let TMP_5 \def (S n0) in (let TMP_6 +\def (CSort n) in (let TMP_7 \def (getl TMP_5 TMP_6 e2) in (clear_gen_sort +TMP_4 n H TMP_7))))))))))))) in (let TMP_52 \def (\lambda (c0: C).(\lambda +(H: ((\forall (e1: C).(\forall (v: T).((clear c0 (CHead e1 (Bind b) v)) \to +(\forall (e2: C).(\forall (n: nat).((getl n e1 e2) \to (getl (S n) c0 +e2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e1: C).(\lambda (v: +T).(\lambda (H0: (clear (CHead c0 k t) (CHead e1 (Bind b) v))).(\lambda (e2: +C).(\lambda (n: nat).(\lambda (H1: (getl n e1 e2)).(let TMP_11 \def (\lambda +(k0: K).((clear (CHead c0 k0 t) (CHead e1 (Bind b) v)) \to (let TMP_9 \def (S +n) in (let TMP_10 \def (CHead c0 k0 t) in (getl TMP_9 TMP_10 e2))))) in (let +TMP_45 \def (\lambda (b0: B).(\lambda (H2: (clear (CHead c0 (Bind b0) t) +(CHead e1 (Bind b) v))).(let TMP_12 \def (\lambda (e: C).(match e with +[(CSort _) \Rightarrow e1 | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_13 +\def (Bind b) in (let TMP_14 \def (CHead e1 TMP_13 v) in (let TMP_15 \def +(Bind b0) in (let TMP_16 \def (CHead c0 TMP_15 t) in (let TMP_17 \def (Bind +b) in (let TMP_18 \def (CHead e1 TMP_17 v) in (let TMP_19 \def +(clear_gen_bind b0 c0 TMP_18 t H2) in (let H3 \def (f_equal C C TMP_12 TMP_14 +TMP_16 TMP_19) in (let TMP_20 \def (\lambda (e: C).(match e with [(CSort _) +\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1) +\Rightarrow b1 | (Flat _) \Rightarrow b])])) in (let TMP_21 \def (Bind b) in +(let TMP_22 \def (CHead e1 TMP_21 v) in (let TMP_23 \def (Bind b0) in (let +TMP_24 \def (CHead c0 TMP_23 t) in (let TMP_25 \def (Bind b) in (let TMP_26 +\def (CHead e1 TMP_25 v) in (let TMP_27 \def (clear_gen_bind b0 c0 TMP_26 t +H2) in (let H4 \def (f_equal C B TMP_20 TMP_22 TMP_24 TMP_27) in (let TMP_28 +\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow v | (CHead _ _ t0) +\Rightarrow t0])) in (let TMP_29 \def (Bind b) in (let TMP_30 \def (CHead e1 +TMP_29 v) in (let TMP_31 \def (Bind b0) in (let TMP_32 \def (CHead c0 TMP_31 +t) in (let TMP_33 \def (Bind b) in (let TMP_34 \def (CHead e1 TMP_33 v) in +(let TMP_35 \def (clear_gen_bind b0 c0 TMP_34 t H2) in (let H5 \def (f_equal +C T TMP_28 TMP_30 TMP_32 TMP_35) in (let TMP_43 \def (\lambda (H6: (eq B b +b0)).(\lambda (H7: (eq C e1 c0)).(let TMP_36 \def (\lambda (c1: C).(getl n c1 +e2)) in (let H8 \def (eq_ind C e1 TMP_36 H1 c0 H7) in (let TMP_40 \def +(\lambda (b1: B).(let TMP_37 \def (S n) in (let TMP_38 \def (Bind b1) in (let +TMP_39 \def (CHead c0 TMP_38 t) in (getl TMP_37 TMP_39 e2))))) in (let TMP_41 +\def (Bind b) in (let TMP_42 \def (getl_head TMP_41 n c0 e2 H8 t) in (eq_ind +B b TMP_40 TMP_42 b0 H6)))))))) in (let TMP_44 \def (TMP_43 H4) in (TMP_44 +H3)))))))))))))))))))))))))))))))) in (let TMP_51 \def (\lambda (f: +F).(\lambda (H2: (clear (CHead c0 (Flat f) t) (CHead e1 (Bind b) v))).(let +TMP_46 \def (S n) in (let TMP_47 \def (Bind b) in (let TMP_48 \def (CHead e1 +TMP_47 v) in (let TMP_49 \def (clear_gen_flat f c0 TMP_48 t H2) in (let +TMP_50 \def (H e1 v TMP_49 e2 n H1) in (getl_flat c0 e2 TMP_46 TMP_50 f +t)))))))) in (K_ind TMP_11 TMP_45 TMP_51 k H0)))))))))))))) in (C_ind TMP_2 +TMP_8 TMP_52 c))))). theorem getl_clear_conf: \forall (i: nat).(\forall (c1: C).(\forall (c3: C).((getl i c1 c3) \to (\forall (c2: C).((clear c1 c2) \to (getl i c2 c3)))))) \def - \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (c3: -C).((getl n c1 c3) \to (\forall (c2: C).((clear c1 c2) \to (getl n c2 -c3))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H: (getl O c1 -c3)).(\lambda (c2: C).(\lambda (H0: (clear c1 c2)).(eq_ind C c3 (\lambda (c: -C).(getl O c c3)) (let H1 \def (clear_gen_all c1 c3 (getl_gen_O c1 c3 H)) in -(ex_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(eq C c3 -(CHead e (Bind b) u))))) (getl O c3 c3) (\lambda (x0: B).(\lambda (x1: -C).(\lambda (x2: T).(\lambda (H2: (eq C c3 (CHead x1 (Bind x0) x2))).(let H3 -\def (eq_ind C c3 (\lambda (c: C).(clear c1 c)) (getl_gen_O c1 c3 H) (CHead -x1 (Bind x0) x2) H2) in (eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c: -C).(getl O c c)) (getl_refl x0 x1 x2) c3 H2)))))) H1)) c2 (clear_mono c1 c3 -(getl_gen_O c1 c3 H) c2 H0))))))) (\lambda (n: nat).(\lambda (_: ((\forall -(c1: C).(\forall (c3: C).((getl n c1 c3) \to (\forall (c2: C).((clear c1 c2) -\to (getl n c2 c3)))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall -(c3: C).((getl (S n) c c3) \to (\forall (c2: C).((clear c c2) \to (getl (S n) -c2 c3)))))) (\lambda (n0: nat).(\lambda (c3: C).(\lambda (H0: (getl (S n) -(CSort n0) c3)).(\lambda (c2: C).(\lambda (_: (clear (CSort n0) -c2)).(getl_gen_sort n0 (S n) c3 H0 (getl (S n) c2 c3))))))) (\lambda (c: -C).(\lambda (H0: ((\forall (c3: C).((getl (S n) c c3) \to (\forall (c2: -C).((clear c c2) \to (getl (S n) c2 c3))))))).(\lambda (k: K).(\lambda (t: -T).(\lambda (c3: C).(\lambda (H1: (getl (S n) (CHead c k t) c3)).(\lambda -(c2: C).(\lambda (H2: (clear (CHead c k t) c2)).(K_ind (\lambda (k0: -K).((getl (S n) (CHead c k0 t) c3) \to ((clear (CHead c k0 t) c2) \to (getl -(S n) c2 c3)))) (\lambda (b: B).(\lambda (H3: (getl (S n) (CHead c (Bind b) -t) c3)).(\lambda (H4: (clear (CHead c (Bind b) t) c2)).(eq_ind_r C (CHead c -(Bind b) t) (\lambda (c0: C).(getl (S n) c0 c3)) (getl_head (Bind b) n c c3 -(getl_gen_S (Bind b) c c3 t n H3) t) c2 (clear_gen_bind b c c2 t H4))))) -(\lambda (f: F).(\lambda (H3: (getl (S n) (CHead c (Flat f) t) c3)).(\lambda -(H4: (clear (CHead c (Flat f) t) c2)).(H0 c3 (getl_gen_S (Flat f) c c3 t n -H3) c2 (clear_gen_flat f c c2 t H4))))) k H1 H2))))))))) c1)))) i). -(* COMMENTS -Initial nodes: 641 -END *) + \lambda (i: nat).(let TMP_1 \def (\lambda (n: nat).(\forall (c1: C).(\forall +(c3: C).((getl n c1 c3) \to (\forall (c2: C).((clear c1 c2) \to (getl n c2 +c3))))))) in (let TMP_20 \def (\lambda (c1: C).(\lambda (c3: C).(\lambda (H: +(getl O c1 c3)).(\lambda (c2: C).(\lambda (H0: (clear c1 c2)).(let TMP_2 \def +(\lambda (c: C).(getl O c c3)) in (let TMP_3 \def (getl_gen_O c1 c3 H) in +(let H1 \def (clear_gen_all c1 c3 TMP_3) in (let TMP_6 \def (\lambda (b: +B).(\lambda (e: C).(\lambda (u: T).(let TMP_4 \def (Bind b) in (let TMP_5 +\def (CHead e TMP_4 u) in (eq C c3 TMP_5)))))) in (let TMP_7 \def (getl O c3 +c3) in (let TMP_16 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: +T).(\lambda (H2: (eq C c3 (CHead x1 (Bind x0) x2))).(let TMP_8 \def (\lambda +(c: C).(clear c1 c)) in (let TMP_9 \def (getl_gen_O c1 c3 H) in (let TMP_10 +\def (Bind x0) in (let TMP_11 \def (CHead x1 TMP_10 x2) in (let H3 \def +(eq_ind C c3 TMP_8 TMP_9 TMP_11 H2) in (let TMP_12 \def (Bind x0) in (let +TMP_13 \def (CHead x1 TMP_12 x2) in (let TMP_14 \def (\lambda (c: C).(getl O +c c)) in (let TMP_15 \def (getl_refl x0 x1 x2) in (eq_ind_r C TMP_13 TMP_14 +TMP_15 c3 H2)))))))))))))) in (let TMP_17 \def (ex_3_ind B C T TMP_6 TMP_7 +TMP_16 H1) in (let TMP_18 \def (getl_gen_O c1 c3 H) in (let TMP_19 \def +(clear_mono c1 c3 TMP_18 c2 H0) in (eq_ind C c3 TMP_2 TMP_17 c2 +TMP_19))))))))))))))) in (let TMP_44 \def (\lambda (n: nat).(\lambda (_: +((\forall (c1: C).(\forall (c3: C).((getl n c1 c3) \to (\forall (c2: +C).((clear c1 c2) \to (getl n c2 c3)))))))).(\lambda (c1: C).(let TMP_22 \def +(\lambda (c: C).(\forall (c3: C).((getl (S n) c c3) \to (\forall (c2: +C).((clear c c2) \to (let TMP_21 \def (S n) in (getl TMP_21 c2 c3))))))) in +(let TMP_26 \def (\lambda (n0: nat).(\lambda (c3: C).(\lambda (H0: (getl (S +n) (CSort n0) c3)).(\lambda (c2: C).(\lambda (_: (clear (CSort n0) c2)).(let +TMP_23 \def (S n) in (let TMP_24 \def (S n) in (let TMP_25 \def (getl TMP_24 +c2 c3) in (getl_gen_sort n0 TMP_23 c3 H0 TMP_25))))))))) in (let TMP_43 \def +(\lambda (c: C).(\lambda (H0: ((\forall (c3: C).((getl (S n) c c3) \to +(\forall (c2: C).((clear c c2) \to (getl (S n) c2 c3))))))).(\lambda (k: +K).(\lambda (t: T).(\lambda (c3: C).(\lambda (H1: (getl (S n) (CHead c k t) +c3)).(\lambda (c2: C).(\lambda (H2: (clear (CHead c k t) c2)).(let TMP_28 +\def (\lambda (k0: K).((getl (S n) (CHead c k0 t) c3) \to ((clear (CHead c k0 +t) c2) \to (let TMP_27 \def (S n) in (getl TMP_27 c2 c3))))) in (let TMP_38 +\def (\lambda (b: B).(\lambda (H3: (getl (S n) (CHead c (Bind b) t) +c3)).(\lambda (H4: (clear (CHead c (Bind b) t) c2)).(let TMP_29 \def (Bind b) +in (let TMP_30 \def (CHead c TMP_29 t) in (let TMP_32 \def (\lambda (c0: +C).(let TMP_31 \def (S n) in (getl TMP_31 c0 c3))) in (let TMP_33 \def (Bind +b) in (let TMP_34 \def (Bind b) in (let TMP_35 \def (getl_gen_S TMP_34 c c3 t +n H3) in (let TMP_36 \def (getl_head TMP_33 n c c3 TMP_35 t) in (let TMP_37 +\def (clear_gen_bind b c c2 t H4) in (eq_ind_r C TMP_30 TMP_32 TMP_36 c2 +TMP_37)))))))))))) in (let TMP_42 \def (\lambda (f: F).(\lambda (H3: (getl (S +n) (CHead c (Flat f) t) c3)).(\lambda (H4: (clear (CHead c (Flat f) t) +c2)).(let TMP_39 \def (Flat f) in (let TMP_40 \def (getl_gen_S TMP_39 c c3 t +n H3) in (let TMP_41 \def (clear_gen_flat f c c2 t H4) in (H0 c3 TMP_40 c2 +TMP_41))))))) in (K_ind TMP_28 TMP_38 TMP_42 k H1 H2)))))))))))) in (C_ind +TMP_22 TMP_26 TMP_43 c1))))))) in (nat_ind TMP_1 TMP_20 TMP_44 i)))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/dec.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/dec.ma index 278362590..f29dc20a5 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/dec.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/dec.ma @@ -14,87 +14,143 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/props.ma". +include "basic_1/getl/props.ma". theorem getl_dec: \forall (c: C).(\forall (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl i c (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c d) \to (\forall (P: Prop).P))))) \def - \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (i: nat).(or (ex_3 C B T -(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b) -v)))))) (\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P)))))) -(\lambda (n: nat).(\lambda (i: nat).(or_intror (ex_3 C B T (\lambda (e: -C).(\lambda (b: B).(\lambda (v: T).(getl i (CSort n) (CHead e (Bind b) -v)))))) (\forall (d: C).((getl i (CSort n) d) \to (\forall (P: Prop).P))) -(\lambda (d: C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P: -Prop).(getl_gen_sort n i d H P))))))) (\lambda (c0: C).(\lambda (H: ((\forall -(i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: -T).(getl i c0 (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c0 d) \to -(\forall (P: Prop).P))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (i: -nat).(nat_ind (\lambda (n: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: -B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall -(d: C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))) (K_ind -(\lambda (k0: K).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: -T).(getl O (CHead c0 k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O -(CHead c0 k0 t) d) \to (\forall (P: Prop).P))))) (\lambda (b: B).(or_introl -(ex_3 C B T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead -c0 (Bind b) t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0 -(Bind b) t) d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e: -C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e -(Bind b0) v))))) c0 b t (getl_refl b c0 t)))) (\lambda (f: F).(let H_x \def -(H O) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: -B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v)))))) (\forall (d: -C).((getl O c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T (\lambda (e: -C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e -(Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to -(\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda (e: C).(\lambda -(b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v))))))).(ex_3_ind C B T -(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) -v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl -O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O -(CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))) (\lambda (x0: -C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O c0 (CHead x0 (Bind -x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: -T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: -C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) (ex_3_intro -C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat -f) t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_flat c0 (CHead x0 (Bind x1) x2) -O H2 f t))))))) H1)) (\lambda (H1: ((\forall (d: C).((getl O c0 d) \to -(\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: C).(\lambda (b: -B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) + \lambda (c: C).(let TMP_6 \def (\lambda (c0: C).(\forall (i: nat).(let TMP_3 +\def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_1 \def (Bind b) +in (let TMP_2 \def (CHead e TMP_1 v) in (getl i c0 TMP_2)))))) in (let TMP_4 +\def (ex_3 C B T TMP_3) in (let TMP_5 \def (\forall (d: C).((getl i c0 d) \to +(\forall (P: Prop).P))) in (or TMP_4 TMP_5)))))) in (let TMP_14 \def (\lambda +(n: nat).(\lambda (i: nat).(let TMP_10 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_7 \def (CSort n) in (let TMP_8 \def (Bind b) in +(let TMP_9 \def (CHead e TMP_8 v) in (getl i TMP_7 TMP_9))))))) in (let +TMP_11 \def (ex_3 C B T TMP_10) in (let TMP_12 \def (\forall (d: C).((getl i +(CSort n) d) \to (\forall (P: Prop).P))) in (let TMP_13 \def (\lambda (d: +C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P: Prop).(getl_gen_sort n i d +H P)))) in (or_intror TMP_11 TMP_12 TMP_13))))))) in (let TMP_159 \def +(\lambda (c0: C).(\lambda (H: ((\forall (i: nat).(or (ex_3 C B T (\lambda (e: +C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b) v)))))) +(\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P))))))).(\lambda (k: +K).(\lambda (t: T).(\lambda (i: nat).(let TMP_21 \def (\lambda (n: nat).(let +TMP_18 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_15 \def +(CHead c0 k t) in (let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead e +TMP_16 v) in (getl n TMP_15 TMP_17))))))) in (let TMP_19 \def (ex_3 C B T +TMP_18) in (let TMP_20 \def (\forall (d: C).((getl n (CHead c0 k t) d) \to +(\forall (P: Prop).P))) in (or TMP_19 TMP_20))))) in (let TMP_28 \def +(\lambda (k0: K).(let TMP_25 \def (\lambda (e: C).(\lambda (b: B).(\lambda +(v: T).(let TMP_22 \def (CHead c0 k0 t) in (let TMP_23 \def (Bind b) in (let +TMP_24 \def (CHead e TMP_23 v) in (getl O TMP_22 TMP_24))))))) in (let TMP_26 +\def (ex_3 C B T TMP_25) in (let TMP_27 \def (\forall (d: C).((getl O (CHead +c0 k0 t) d) \to (\forall (P: Prop).P))) in (or TMP_26 TMP_27))))) in (let +TMP_43 \def (\lambda (b: B).(let TMP_33 \def (\lambda (e: C).(\lambda (b0: +B).(\lambda (v: T).(let TMP_29 \def (Bind b) in (let TMP_30 \def (CHead c0 +TMP_29 t) in (let TMP_31 \def (Bind b0) in (let TMP_32 \def (CHead e TMP_31 +v) in (getl O TMP_30 TMP_32)))))))) in (let TMP_34 \def (ex_3 C B T TMP_33) +in (let TMP_35 \def (\forall (d: C).((getl O (CHead c0 (Bind b) t) d) \to +(\forall (P: Prop).P))) in (let TMP_40 \def (\lambda (e: C).(\lambda (b0: +B).(\lambda (v: T).(let TMP_36 \def (Bind b) in (let TMP_37 \def (CHead c0 +TMP_36 t) in (let TMP_38 \def (Bind b0) in (let TMP_39 \def (CHead e TMP_38 +v) in (getl O TMP_37 TMP_39)))))))) in (let TMP_41 \def (getl_refl b c0 t) in +(let TMP_42 \def (ex_3_intro C B T TMP_40 c0 b t TMP_41) in (or_introl TMP_34 +TMP_35 TMP_42)))))))) in (let TMP_101 \def (\lambda (f: F).(let H_x \def (H +O) in (let H0 \def H_x in (let TMP_46 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_44 \def (Bind b) in (let TMP_45 \def (CHead e +TMP_44 v) in (getl O c0 TMP_45)))))) in (let TMP_47 \def (ex_3 C B T TMP_46) +in (let TMP_48 \def (\forall (d: C).((getl O c0 d) \to (\forall (P: +Prop).P))) in (let TMP_53 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v: +T).(let TMP_49 \def (Flat f) in (let TMP_50 \def (CHead c0 TMP_49 t) in (let +TMP_51 \def (Bind b) in (let TMP_52 \def (CHead e TMP_51 v) in (getl O TMP_50 +TMP_52)))))))) in (let TMP_54 \def (ex_3 C B T TMP_53) in (let TMP_55 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) -(\lambda (d: C).(\lambda (H2: (getl O (CHead c0 (Flat f) t) d)).(\lambda (P: -Prop).(H1 d (getl_intro O c0 d c0 (drop_refl c0) (clear_gen_flat f c0 d t -(getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))) k) (\lambda (n: -nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda -(v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: -C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))).(let H_x \def (H -(r k n)) in (let H1 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda -(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v)))))) (\forall -(d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T -(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) -(CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to -(\forall (P: Prop).P)))) (\lambda (H2: (ex_3 C B T (\lambda (e: C).(\lambda -(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v))))))).(ex_3_ind -C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead -e (Bind b) v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda -(v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: -C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (x0: -C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H3: (getl (r k n) c0 (CHead x0 -(Bind x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: -B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) -(\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P))) -(ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) -(CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k n c0 (CHead x0 -(Bind x1) x2) H3 t))))))) H2)) (\lambda (H2: ((\forall (d: C).((getl (r k n) -c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: -C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind -b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: -Prop).P))) (\lambda (d: C).(\lambda (H3: (getl (S n) (CHead c0 k t) -d)).(\lambda (P: Prop).(H2 d (getl_gen_S k c0 d t n H3) P)))))) H1))))) -i)))))) c). -(* COMMENTS -Initial nodes: 1563 -END *) +in (let TMP_56 \def (or TMP_54 TMP_55) in (let TMP_85 \def (\lambda (H1: +(ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead +e (Bind b) v))))))).(let TMP_59 \def (\lambda (e: C).(\lambda (b: B).(\lambda +(v: T).(let TMP_57 \def (Bind b) in (let TMP_58 \def (CHead e TMP_57 v) in +(getl O c0 TMP_58)))))) in (let TMP_64 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_60 \def (Flat f) in (let TMP_61 \def (CHead c0 +TMP_60 t) in (let TMP_62 \def (Bind b) in (let TMP_63 \def (CHead e TMP_62 v) +in (getl O TMP_61 TMP_63)))))))) in (let TMP_65 \def (ex_3 C B T TMP_64) in +(let TMP_66 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to +(\forall (P: Prop).P))) in (let TMP_67 \def (or TMP_65 TMP_66) in (let TMP_84 +\def (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O +c0 (CHead x0 (Bind x1) x2))).(let TMP_72 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_68 \def (Flat f) in (let TMP_69 \def (CHead c0 +TMP_68 t) in (let TMP_70 \def (Bind b) in (let TMP_71 \def (CHead e TMP_70 v) +in (getl O TMP_69 TMP_71)))))))) in (let TMP_73 \def (ex_3 C B T TMP_72) in +(let TMP_74 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to +(\forall (P: Prop).P))) in (let TMP_79 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_75 \def (Flat f) in (let TMP_76 \def (CHead c0 +TMP_75 t) in (let TMP_77 \def (Bind b) in (let TMP_78 \def (CHead e TMP_77 v) +in (getl O TMP_76 TMP_78)))))))) in (let TMP_80 \def (Bind x1) in (let TMP_81 +\def (CHead x0 TMP_80 x2) in (let TMP_82 \def (getl_flat c0 TMP_81 O H2 f t) +in (let TMP_83 \def (ex_3_intro C B T TMP_79 x0 x1 x2 TMP_82) in (or_introl +TMP_73 TMP_74 TMP_83))))))))))))) in (ex_3_ind C B T TMP_59 TMP_67 TMP_84 +H1)))))))) in (let TMP_100 \def (\lambda (H1: ((\forall (d: C).((getl O c0 d) +\to (\forall (P: Prop).P))))).(let TMP_90 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_86 \def (Flat f) in (let TMP_87 \def (CHead c0 +TMP_86 t) in (let TMP_88 \def (Bind b) in (let TMP_89 \def (CHead e TMP_88 v) +in (getl O TMP_87 TMP_89)))))))) in (let TMP_91 \def (ex_3 C B T TMP_90) in +(let TMP_92 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to +(\forall (P: Prop).P))) in (let TMP_99 \def (\lambda (d: C).(\lambda (H2: +(getl O (CHead c0 (Flat f) t) d)).(\lambda (P: Prop).(let TMP_93 \def +(drop_refl c0) in (let TMP_94 \def (Flat f) in (let TMP_95 \def (CHead c0 +TMP_94 t) in (let TMP_96 \def (getl_gen_O TMP_95 d H2) in (let TMP_97 \def +(clear_gen_flat f c0 d t TMP_96) in (let TMP_98 \def (getl_intro O c0 d c0 +TMP_93 TMP_97) in (H1 d TMP_98 P)))))))))) in (or_intror TMP_91 TMP_92 +TMP_99)))))) in (or_ind TMP_47 TMP_48 TMP_56 TMP_85 TMP_100 H0))))))))))))) +in (let TMP_102 \def (K_ind TMP_28 TMP_43 TMP_101 k) in (let TMP_158 \def +(\lambda (n: nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall +(d: C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))).(let TMP_103 +\def (r k n) in (let H_x \def (H TMP_103) in (let H1 \def H_x in (let TMP_107 +\def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_104 \def (r k +n) in (let TMP_105 \def (Bind b) in (let TMP_106 \def (CHead e TMP_105 v) in +(getl TMP_104 c0 TMP_106))))))) in (let TMP_108 \def (ex_3 C B T TMP_107) in +(let TMP_109 \def (\forall (d: C).((getl (r k n) c0 d) \to (\forall (P: +Prop).P))) in (let TMP_114 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v: +T).(let TMP_110 \def (S n) in (let TMP_111 \def (CHead c0 k t) in (let +TMP_112 \def (Bind b) in (let TMP_113 \def (CHead e TMP_112 v) in (getl +TMP_110 TMP_111 TMP_113)))))))) in (let TMP_115 \def (ex_3 C B T TMP_114) in +(let TMP_116 \def (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall +(P: Prop).P))) in (let TMP_117 \def (or TMP_115 TMP_116) in (let TMP_147 \def +(\lambda (H2: (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: +T).(getl (r k n) c0 (CHead e (Bind b) v))))))).(let TMP_121 \def (\lambda (e: +C).(\lambda (b: B).(\lambda (v: T).(let TMP_118 \def (r k n) in (let TMP_119 +\def (Bind b) in (let TMP_120 \def (CHead e TMP_119 v) in (getl TMP_118 c0 +TMP_120))))))) in (let TMP_126 \def (\lambda (e: C).(\lambda (b: B).(\lambda +(v: T).(let TMP_122 \def (S n) in (let TMP_123 \def (CHead c0 k t) in (let +TMP_124 \def (Bind b) in (let TMP_125 \def (CHead e TMP_124 v) in (getl +TMP_122 TMP_123 TMP_125)))))))) in (let TMP_127 \def (ex_3 C B T TMP_126) in +(let TMP_128 \def (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall +(P: Prop).P))) in (let TMP_129 \def (or TMP_127 TMP_128) in (let TMP_146 \def +(\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H3: (getl (r k +n) c0 (CHead x0 (Bind x1) x2))).(let TMP_134 \def (\lambda (e: C).(\lambda +(b: B).(\lambda (v: T).(let TMP_130 \def (S n) in (let TMP_131 \def (CHead c0 +k t) in (let TMP_132 \def (Bind b) in (let TMP_133 \def (CHead e TMP_132 v) +in (getl TMP_130 TMP_131 TMP_133)))))))) in (let TMP_135 \def (ex_3 C B T +TMP_134) in (let TMP_136 \def (\forall (d: C).((getl (S n) (CHead c0 k t) d) +\to (\forall (P: Prop).P))) in (let TMP_141 \def (\lambda (e: C).(\lambda (b: +B).(\lambda (v: T).(let TMP_137 \def (S n) in (let TMP_138 \def (CHead c0 k +t) in (let TMP_139 \def (Bind b) in (let TMP_140 \def (CHead e TMP_139 v) in +(getl TMP_137 TMP_138 TMP_140)))))))) in (let TMP_142 \def (Bind x1) in (let +TMP_143 \def (CHead x0 TMP_142 x2) in (let TMP_144 \def (getl_head k n c0 +TMP_143 H3 t) in (let TMP_145 \def (ex_3_intro C B T TMP_141 x0 x1 x2 +TMP_144) in (or_introl TMP_135 TMP_136 TMP_145))))))))))))) in (ex_3_ind C B +T TMP_121 TMP_129 TMP_146 H2)))))))) in (let TMP_157 \def (\lambda (H2: +((\forall (d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))))).(let +TMP_152 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_148 +\def (S n) in (let TMP_149 \def (CHead c0 k t) in (let TMP_150 \def (Bind b) +in (let TMP_151 \def (CHead e TMP_150 v) in (getl TMP_148 TMP_149 +TMP_151)))))))) in (let TMP_153 \def (ex_3 C B T TMP_152) in (let TMP_154 +\def (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: +Prop).P))) in (let TMP_156 \def (\lambda (d: C).(\lambda (H3: (getl (S n) +(CHead c0 k t) d)).(\lambda (P: Prop).(let TMP_155 \def (getl_gen_S k c0 d t +n H3) in (H2 d TMP_155 P))))) in (or_intror TMP_153 TMP_154 TMP_156)))))) in +(or_ind TMP_108 TMP_109 TMP_117 TMP_147 TMP_157 H1))))))))))))))) in (nat_ind +TMP_21 TMP_102 TMP_158 i)))))))))))) in (C_ind TMP_6 TMP_14 TMP_159 c)))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/defs.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/defs.ma index a6efd2eee..9a21c5ece 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/defs.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/defs.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/drop/defs.ma". +include "basic_1/drop/defs.ma". -include "Basic-1/clear/defs.ma". +include "basic_1/clear/defs.ma". inductive getl (h: nat) (c1: C) (c2: C): Prop \def | getl_intro: \forall (e: C).((drop h O c1 e) \to ((clear e c2) \to (getl h diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/drop.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/drop.ma index e4404e137..9fba2b7b1 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/drop.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/drop.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/props.ma". +include "basic_1/getl/props.ma". -include "Basic-1/clear/drop.ma". +include "basic_1/clear/drop.ma". theorem getl_drop: \forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (h: @@ -35,33 +35,28 @@ T).(\lambda (h: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t) (getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear (CHead c0 k0 t) (CHead e (Bind b) u)) \to (drop (S O) O (CHead c0 k0 t) e))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e (Bind -b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 in C return -(\lambda (_: C).C) with [(CSort _) \Rightarrow e | (CHead c1 _ _) \Rightarrow -c1])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 -(CHead e (Bind b) u) t H1)) in ((let H3 \def (f_equal C B (\lambda (e0: -C).(match e0 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | -(CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with -[(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) -(CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in -((let H4 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda -(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) -(CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e -(Bind b) u) t H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e -c0)).(eq_ind_r C c0 (\lambda (c1: C).(drop (S O) O (CHead c0 (Bind b0) t) -c1)) (eq_ind B b (\lambda (b1: B).(drop (S O) O (CHead c0 (Bind b1) t) c0)) -(drop_drop (Bind b) O c0 c0 (drop_refl c0) t) b0 H5) e H6)))) H3)) H2)))) -(\lambda (f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) -u))).(drop_clear_O b (CHead c0 (Flat f) t) e u (clear_flat c0 (CHead e (Bind -b) u) (clear_gen_flat f c0 (CHead e (Bind b) u) t H1) f t) e O (drop_refl -e)))) k (getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n: -nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (drop (S -n) O (CHead c0 k t) e)))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead e -(Bind b) u))).(drop_drop k (S n) c0 e (eq_ind_r nat (S (r k n)) (\lambda (n0: -nat).(drop n0 O c0 e)) (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind b) u) t -n H1)) (r k (S n)) (r_S k n)) t)))) h)))))))) c)). -(* COMMENTS -Initial nodes: 827 -END *) +b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _) +\Rightarrow e | (CHead c1 _ _) \Rightarrow c1])) (CHead e (Bind b) u) (CHead +c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in ((let H3 +\def (f_equal C B (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow b | +(CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1) \Rightarrow b1 | (Flat +_) \Rightarrow b])])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) +(clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in ((let H4 \def (f_equal C +T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | (CHead _ _ t0) +\Rightarrow t0])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind +b0 c0 (CHead e (Bind b) u) t H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: +(eq C e c0)).(eq_ind_r C c0 (\lambda (c1: C).(drop (S O) O (CHead c0 (Bind +b0) t) c1)) (eq_ind B b (\lambda (b1: B).(drop (S O) O (CHead c0 (Bind b1) t) +c0)) (drop_drop (Bind b) O c0 c0 (drop_refl c0) t) b0 H5) e H6)))) H3)) +H2)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e +(Bind b) u))).(drop_clear_O b (CHead c0 (Flat f) t) e u (clear_flat c0 (CHead +e (Bind b) u) (clear_gen_flat f c0 (CHead e (Bind b) u) t H1) f t) e O +(drop_refl e)))) k (getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) +(\lambda (n: nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) +\to (drop (S n) O (CHead c0 k t) e)))).(\lambda (H1: (getl (S n) (CHead c0 k +t) (CHead e (Bind b) u))).(drop_drop k (S n) c0 e (eq_ind_r nat (S (r k n)) +(\lambda (n0: nat).(drop n0 O c0 e)) (H e u (r k n) (getl_gen_S k c0 (CHead e +(Bind b) u) t n H1)) (r k (S n)) (r_S k n)) t)))) h)))))))) c)). theorem getl_drop_conf_lt: \forall (b: B).(\forall (c: C).(\forall (c0: C).(\forall (u: T).(\forall (i: @@ -119,34 +114,33 @@ K).((drop i O (CHead c0 k t) (CHead x0 k1 t0)) \to ((clear (CHead x0 k1 t0) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) (\lambda (b0: B).(\lambda (H7: (drop i O (CHead c0 k t) (CHead x0 (Bind b0) t0))).(\lambda (H8: (clear (CHead x0 (Bind b0) t0) (CHead c1 (Bind b) u))).(let H9 \def -(f_equal C C (\lambda (e0: C).(match e0 in C return (\lambda (_: C).C) with -[(CSort _) \Rightarrow c1 | (CHead c2 _ _) \Rightarrow c2])) (CHead c1 (Bind -b) u) (CHead x0 (Bind b0) t0) (clear_gen_bind b0 x0 (CHead c1 (Bind b) u) t0 -H8)) in ((let H10 \def (f_equal C B (\lambda (e0: C).(match e0 in C return -(\lambda (_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k1 _) \Rightarrow -(match k1 in K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | -(Flat _) \Rightarrow b])])) (CHead c1 (Bind b) u) (CHead x0 (Bind b0) t0) +(f_equal C C (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow c1 | +(CHead c2 _ _) \Rightarrow c2])) (CHead c1 (Bind b) u) (CHead x0 (Bind b0) +t0) (clear_gen_bind b0 x0 (CHead c1 (Bind b) u) t0 H8)) in ((let H10 \def +(f_equal C B (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow b | +(CHead _ k1 _) \Rightarrow (match k1 with [(Bind b1) \Rightarrow b1 | (Flat +_) \Rightarrow b])])) (CHead c1 (Bind b) u) (CHead x0 (Bind b0) t0) (clear_gen_bind b0 x0 (CHead c1 (Bind b) u) t0 H8)) in ((let H11 \def -(f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T) with -[(CSort _) \Rightarrow u | (CHead _ _ t1) \Rightarrow t1])) (CHead c1 (Bind -b) u) (CHead x0 (Bind b0) t0) (clear_gen_bind b0 x0 (CHead c1 (Bind b) u) t0 -H8)) in (\lambda (H12: (eq B b b0)).(\lambda (H13: (eq C c1 x0)).(let H14 -\def (eq_ind_r T t0 (\lambda (t1: T).(drop i O (CHead c0 k t) (CHead x0 (Bind -b0) t1))) H7 u H11) in (let H15 \def (eq_ind_r B b0 (\lambda (b1: B).(drop i -O (CHead c0 k t) (CHead x0 (Bind b1) u))) H14 b H12) in (let H16 \def -(eq_ind_r C x0 (\lambda (c2: C).((drop i O (CHead c0 k t) c2) \to ((clear c2 -(CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u -(lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl i e (CHead e0 (Bind b) -v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) IHx c1 H13) in -(let H17 \def (eq_ind_r C x0 (\lambda (c2: C).(drop i O (CHead c0 k t) (CHead -c2 (Bind b) u))) H15 c1 H13) in (ex3_2_ind T C (\lambda (v: T).(\lambda (_: -C).(eq T u (lift h (r (Bind b) d) v)))) (\lambda (v: T).(\lambda (e0: -C).(drop i O e (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: -C).(drop h (r (Bind b) d) c1 e0))) (ex3_2 T C (\lambda (v: T).(\lambda (_: -C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl i e (CHead -e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0)))) -(\lambda (x1: T).(\lambda (x2: C).(\lambda (H18: (eq T u (lift h (r (Bind b) -d) x1))).(\lambda (H19: (drop i O e (CHead x2 (Bind b) x1))).(\lambda (H20: +(f_equal C T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | +(CHead _ _ t1) \Rightarrow t1])) (CHead c1 (Bind b) u) (CHead x0 (Bind b0) +t0) (clear_gen_bind b0 x0 (CHead c1 (Bind b) u) t0 H8)) in (\lambda (H12: (eq +B b b0)).(\lambda (H13: (eq C c1 x0)).(let H14 \def (eq_ind_r T t0 (\lambda +(t1: T).(drop i O (CHead c0 k t) (CHead x0 (Bind b0) t1))) H7 u H11) in (let +H15 \def (eq_ind_r B b0 (\lambda (b1: B).(drop i O (CHead c0 k t) (CHead x0 +(Bind b1) u))) H14 b H12) in (let H16 \def (eq_ind_r C x0 (\lambda (c2: +C).((drop i O (CHead c0 k t) c2) \to ((clear c2 (CHead c1 (Bind b) u)) \to +(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda +(v: T).(\lambda (e0: C).(getl i e (CHead e0 (Bind b) v)))) (\lambda (_: +T).(\lambda (e0: C).(drop h d c1 e0))))))) IHx c1 H13) in (let H17 \def +(eq_ind_r C x0 (\lambda (c2: C).(drop i O (CHead c0 k t) (CHead c2 (Bind b) +u))) H15 c1 H13) in (ex3_2_ind T C (\lambda (v: T).(\lambda (_: C).(eq T u +(lift h (r (Bind b) d) v)))) (\lambda (v: T).(\lambda (e0: C).(drop i O e +(CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h (r (Bind b) +d) c1 e0))) (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d +v)))) (\lambda (v: T).(\lambda (e0: C).(getl i e (CHead e0 (Bind b) v)))) +(\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0)))) (\lambda (x1: +T).(\lambda (x2: C).(\lambda (H18: (eq T u (lift h (r (Bind b) d) +x1))).(\lambda (H19: (drop i O e (CHead x2 (Bind b) x1))).(\lambda (H20: (drop h (r (Bind b) d) c1 x2)).(let H21 \def (eq_ind T u (\lambda (t1: T).((drop i O (CHead c0 k t) c1) \to ((clear c1 (CHead c1 (Bind b) t1)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T t1 (lift h d v)))) (\lambda @@ -177,83 +171,81 @@ e)).(\lambda (H10: (drop O O (CHead c0 k t) (CHead x0 (Flat f) t0))).(\lambda \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O e (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0)))))))).(let H11 \def (f_equal C C -(\lambda (e0: C).(match e0 in C return (\lambda (_: C).C) with [(CSort _) -\Rightarrow c0 | (CHead c2 _ _) \Rightarrow c2])) (CHead c0 k t) (CHead x0 -(Flat f) t0) (drop_gen_refl (CHead c0 k t) (CHead x0 (Flat f) t0) H10)) in -((let H12 \def (f_equal C K (\lambda (e0: C).(match e0 in C return (\lambda -(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k1 _) \Rightarrow k1])) +(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow c0 | (CHead c2 _ _) +\Rightarrow c2])) (CHead c0 k t) (CHead x0 (Flat f) t0) (drop_gen_refl (CHead +c0 k t) (CHead x0 (Flat f) t0) H10)) in ((let H12 \def (f_equal C K (\lambda +(e0: C).(match e0 with [(CSort _) \Rightarrow k | (CHead _ k1 _) \Rightarrow +k1])) (CHead c0 k t) (CHead x0 (Flat f) t0) (drop_gen_refl (CHead c0 k t) +(CHead x0 (Flat f) t0) H10)) in ((let H13 \def (f_equal C T (\lambda (e0: +C).(match e0 with [(CSort _) \Rightarrow t | (CHead _ _ t1) \Rightarrow t1])) (CHead c0 k t) (CHead x0 (Flat f) t0) (drop_gen_refl (CHead c0 k t) (CHead x0 -(Flat f) t0) H10)) in ((let H13 \def (f_equal C T (\lambda (e0: C).(match e0 -in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow t | (CHead _ _ t1) -\Rightarrow t1])) (CHead c0 k t) (CHead x0 (Flat f) t0) (drop_gen_refl (CHead -c0 k t) (CHead x0 (Flat f) t0) H10)) in (\lambda (H14: (eq K k (Flat -f))).(\lambda (H15: (eq C c0 x0)).(let H16 \def (eq_ind_r C x0 (\lambda (c2: -C).(clear c2 (CHead c1 (Bind b) u))) (clear_gen_flat f x0 (CHead c1 (Bind b) -u) t0 H8) c0 H15) in (let H17 \def (eq_ind_r C x0 (\lambda (c2: C).((drop O O -(CHead c0 k t) c2) \to ((clear c2 (CHead c1 (Bind b) u)) \to (ex3_2 T C +(Flat f) t0) H10)) in (\lambda (H14: (eq K k (Flat f))).(\lambda (H15: (eq C +c0 x0)).(let H16 \def (eq_ind_r C x0 (\lambda (c2: C).(clear c2 (CHead c1 +(Bind b) u))) (clear_gen_flat f x0 (CHead c1 (Bind b) u) t0 H8) c0 H15) in +(let H17 \def (eq_ind_r C x0 (\lambda (c2: C).((drop O O (CHead c0 k t) c2) +\to ((clear c2 (CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda +(_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O e +(CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 +e0))))))) IHx0 c0 H15) in (let H18 \def (eq_ind K k (\lambda (k1: K).((drop O +O (CHead c0 k1 t) c0) \to ((clear c0 (CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O e (CHead e0 (Bind b) v)))) (\lambda (_: -T).(\lambda (e0: C).(drop h d c1 e0))))))) IHx0 c0 H15) in (let H18 \def -(eq_ind K k (\lambda (k1: K).((drop O O (CHead c0 k1 t) c0) \to ((clear c0 -(CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u +T).(\lambda (e0: C).(drop h d c1 e0))))))) H17 (Flat f) H14) in (let H19 \def +(eq_ind K k (\lambda (k1: K).(drop h (S (plus O d)) (CHead c0 k1 t) e)) H9 +(Flat f) H14) in (ex3_2_ind C T (\lambda (e0: C).(\lambda (v: T).(eq C e +(CHead e0 (Flat f) v)))) (\lambda (_: C).(\lambda (v: T).(eq T t (lift h (r +(Flat f) (plus O d)) v)))) (\lambda (e0: C).(\lambda (_: T).(drop h (r (Flat +f) (plus O d)) c0 e0))) (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O e (CHead e0 (Bind b) -v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H17 (Flat f) -H14) in (let H19 \def (eq_ind K k (\lambda (k1: K).(drop h (S (plus O d)) -(CHead c0 k1 t) e)) H9 (Flat f) H14) in (ex3_2_ind C T (\lambda (e0: -C).(\lambda (v: T).(eq C e (CHead e0 (Flat f) v)))) (\lambda (_: C).(\lambda -(v: T).(eq T t (lift h (r (Flat f) (plus O d)) v)))) (\lambda (e0: -C).(\lambda (_: T).(drop h (r (Flat f) (plus O d)) c0 e0))) (ex3_2 T C -(\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: -T).(\lambda (e0: C).(getl O e (CHead e0 (Bind b) v)))) (\lambda (_: -T).(\lambda (e0: C).(drop h d c1 e0)))) (\lambda (x1: C).(\lambda (x2: -T).(\lambda (H20: (eq C e (CHead x1 (Flat f) x2))).(\lambda (H21: (eq T t -(lift h (r (Flat f) (plus O d)) x2))).(\lambda (H22: (drop h (r (Flat f) -(plus O d)) c0 x1)).(let H23 \def (f_equal T T (\lambda (e0: T).e0) t (lift h -(r (Flat f) (plus O d)) x2) H21) in (let H24 \def (eq_ind C e (\lambda (c2: -C).((drop O O (CHead c0 (Flat f) t) c0) \to ((clear c0 (CHead c1 (Bind b) u)) -\to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) +v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0)))) (\lambda (x1: +C).(\lambda (x2: T).(\lambda (H20: (eq C e (CHead x1 (Flat f) x2))).(\lambda +(H21: (eq T t (lift h (r (Flat f) (plus O d)) x2))).(\lambda (H22: (drop h (r +(Flat f) (plus O d)) c0 x1)).(let H23 \def (f_equal T T (\lambda (e0: T).e0) +t (lift h (r (Flat f) (plus O d)) x2) H21) in (let H24 \def (eq_ind C e +(\lambda (c2: C).((drop O O (CHead c0 (Flat f) t) c0) \to ((clear c0 (CHead +c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift +h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O c2 (CHead e0 (Bind b) +v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H18 (CHead x1 +(Flat f) x2) H20) in (eq_ind_r C (CHead x1 (Flat f) x2) (\lambda (c2: +C).(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O c2 (CHead e0 (Bind b) v)))) (\lambda -(_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H18 (CHead x1 (Flat f) x2) -H20) in (eq_ind_r C (CHead x1 (Flat f) x2) (\lambda (c2: C).(ex3_2 T C +(_: T).(\lambda (e0: C).(drop h d c1 e0))))) (let H25 \def (eq_ind T t +(\lambda (t1: T).((drop O O (CHead c0 (Flat f) t1) c0) \to ((clear c0 (CHead +c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift +h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) +(CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 +e0))))))) H24 (lift h (S d) x2) H23) in (let H26 \def (H c1 u O (getl_intro O +c0 (CHead c1 (Bind b) u) c0 (drop_refl c0) H16) x1 h d H22) in (ex3_2_ind T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: -T).(\lambda (e0: C).(getl O c2 (CHead e0 (Bind b) v)))) (\lambda (_: -T).(\lambda (e0: C).(drop h d c1 e0))))) (let H25 \def (eq_ind T t (\lambda -(t1: T).((drop O O (CHead c0 (Flat f) t1) c0) \to ((clear c0 (CHead c1 (Bind -b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) -(\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) (CHead e0 -(Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H24 -(lift h (S d) x2) H23) in (let H26 \def (H c1 u O (getl_intro O c0 (CHead c1 -(Bind b) u) c0 (drop_refl c0) H16) x1 h d H22) in (ex3_2_ind T C (\lambda (v: -T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: -C).(getl O x1 (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop -h d c1 e0))) (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d -v)))) (\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) (CHead -e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0)))) -(\lambda (x3: T).(\lambda (x4: C).(\lambda (H27: (eq T u (lift h d -x3))).(\lambda (H28: (getl O x1 (CHead x4 (Bind b) x3))).(\lambda (H29: (drop -h d c1 x4)).(let H30 \def (eq_ind T u (\lambda (t1: T).((drop O O (CHead c0 -(Flat f) (lift h (S d) x2)) c0) \to ((clear c0 (CHead c1 (Bind b) t1)) \to -(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T t1 (lift h d v)))) (\lambda -(v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) (CHead e0 (Bind b) -v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H25 (lift h d -x3) H27) in (let H31 \def (eq_ind T u (\lambda (t1: T).(clear c0 (CHead c1 -(Bind b) t1))) H16 (lift h d x3) H27) in (eq_ind_r T (lift h d x3) (\lambda -(t1: T).(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T t1 (lift h d v)))) +T).(\lambda (e0: C).(getl O x1 (CHead e0 (Bind b) v)))) (\lambda (_: +T).(\lambda (e0: C).(drop h d c1 e0))) (ex3_2 T C (\lambda (v: T).(\lambda +(_: C).(eq T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O +(CHead x1 (Flat f) x2) (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: +C).(drop h d c1 e0)))) (\lambda (x3: T).(\lambda (x4: C).(\lambda (H27: (eq T +u (lift h d x3))).(\lambda (H28: (getl O x1 (CHead x4 (Bind b) x3))).(\lambda +(H29: (drop h d c1 x4)).(let H30 \def (eq_ind T u (\lambda (t1: T).((drop O O +(CHead c0 (Flat f) (lift h (S d) x2)) c0) \to ((clear c0 (CHead c1 (Bind b) +t1)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T t1 (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) (CHead e0 -(Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))) -(ex3_2_intro T C (\lambda (v: T).(\lambda (_: C).(eq T (lift h d x3) (lift h +(Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) H25 +(lift h d x3) H27) in (let H31 \def (eq_ind T u (\lambda (t1: T).(clear c0 +(CHead c1 (Bind b) t1))) H16 (lift h d x3) H27) in (eq_ind_r T (lift h d x3) +(\lambda (t1: T).(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T t1 (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) x2) -(CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))) -x3 x4 (refl_equal T (lift h d x3)) (getl_flat x1 (CHead x4 (Bind b) x3) O H28 -f x2) H29) u H27)))))))) H26))) e H20)))))))) (drop_gen_skip_l c0 e t h (plus -O d) (Flat f) H19))))))))) H12)) H11))))) (\lambda (i0: nat).(\lambda (IHi: -(((drop h (S (plus i0 d)) (CHead c0 k t) e) \to ((drop i0 O (CHead c0 k t) -(CHead x0 (Flat f) t0)) \to ((((drop i0 O (CHead c0 k t) x0) \to ((clear x0 -(CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u -(lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl i0 e (CHead e0 (Bind -b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) \to (ex3_2 T -C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda (v: -T).(\lambda (e0: C).(getl i0 e (CHead e0 (Bind b) v)))) (\lambda (_: +(CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 +e0))))) (ex3_2_intro T C (\lambda (v: T).(\lambda (_: C).(eq T (lift h d x3) +(lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl O (CHead x1 (Flat f) +x2) (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 +e0))) x3 x4 (refl_equal T (lift h d x3)) (getl_flat x1 (CHead x4 (Bind b) x3) +O H28 f x2) H29) u H27)))))))) H26))) e H20)))))))) (drop_gen_skip_l c0 e t h +(plus O d) (Flat f) H19))))))))) H12)) H11))))) (\lambda (i0: nat).(\lambda +(IHi: (((drop h (S (plus i0 d)) (CHead c0 k t) e) \to ((drop i0 O (CHead c0 k +t) (CHead x0 (Flat f) t0)) \to ((((drop i0 O (CHead c0 k t) x0) \to ((clear +x0 (CHead c1 (Bind b) u)) \to (ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq +T u (lift h d v)))) (\lambda (v: T).(\lambda (e0: C).(getl i0 e (CHead e0 +(Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))) \to +(ex3_2 T C (\lambda (v: T).(\lambda (_: C).(eq T u (lift h d v)))) (\lambda +(v: T).(\lambda (e0: C).(getl i0 e (CHead e0 (Bind b) v)))) (\lambda (_: T).(\lambda (e0: C).(drop h d c1 e0))))))))).(\lambda (H9: (drop h (S (plus (S i0) d)) (CHead c0 k t) e)).(\lambda (H10: (drop (S i0) O (CHead c0 k t) (CHead x0 (Flat f) t0))).(\lambda (IHx0: (((drop (S i0) O (CHead c0 k t) x0) @@ -332,9 +324,6 @@ T).(\lambda (e0: C).(getl (S i0) (CHead x1 k x2) (CHead e0 (Bind b) v)))) h d x3)) (getl_head k i0 x1 (CHead x4 (Bind b) x3) H23 x2) H24) u H22)))))))) H21)))))) e H11))))))))) (drop_gen_skip_l c0 e t h (plus (S i0) d) k H9))))))) i H1 H7 IHx)))) k0 H5 H6))))))) x H3 H4)))) H2)))))))))))))) c)). -(* COMMENTS -Initial nodes: 6137 -END *) theorem getl_drop_conf_ge: \forall (i: nat).(\forall (a: C).(\forall (c: C).((getl i c a) \to (\forall @@ -348,9 +337,6 @@ in (ex2_ind C (\lambda (e0: C).(drop i O c e0)) (\lambda (e0: C).(clear e0 a)) (getl (minus i h) e a) (\lambda (x: C).(\lambda (H3: (drop i O c x)).(\lambda (H4: (clear x a)).(getl_intro (minus i h) e a x (drop_conf_ge i x c H3 e h d H0 H1) H4)))) H2)))))))))). -(* COMMENTS -Initial nodes: 141 -END *) theorem getl_conf_ge_drop: \forall (b: B).(\forall (c1: C).(\forall (e: C).(\forall (u: T).(\forall (i: @@ -364,9 +350,6 @@ nat).(\lambda (H: (getl i c1 (CHead e (Bind b) u))).(\lambda (c2: C).(\lambda u i H) c2 (S O) i H0 (eq_ind_r nat (plus (S O) i) (\lambda (n: nat).(le n (S i))) (le_n (S i)) (plus i (S O)) (plus_sym i (S O)))) i (minus_Sx_SO i)) in H3)))))))). -(* COMMENTS -Initial nodes: 151 -END *) theorem getl_drop_conf_rev: \forall (j: nat).(\forall (e1: C).(\forall (e2: C).((drop j O e1 e2) \to @@ -378,9 +361,6 @@ c2 (CHead e2 (Bind b) v2)) \to (ex2 C (\lambda (c1: C).(drop j O c1 c2)) e2)).(\lambda (b: B).(\lambda (c2: C).(\lambda (v2: T).(\lambda (i: nat).(\lambda (H0: (getl i c2 (CHead e2 (Bind b) v2))).(drop_conf_rev j e1 e2 H c2 (S i) (getl_drop b c2 e2 v2 i H0)))))))))). -(* COMMENTS -Initial nodes: 69 -END *) theorem drop_getl_trans_lt: \forall (i: nat).(\forall (d: nat).((lt i d) \to (\forall (c1: C).(\forall @@ -412,11 +392,9 @@ e2 v H4) in (ex2_ind C (\lambda (c3: C).(clear x0 (CHead c3 (Bind b) (lift h (H10: (drop h (minus d (S i)) x1 e2)).(ex_intro2 C (\lambda (e1: C).(getl i c1 (CHead e1 (Bind b) (lift h (minus d (S i)) v)))) (\lambda (e1: C).(drop h (minus d (S i)) e1 e2)) x1 (getl_intro i c1 (CHead x1 (Bind b) (lift h (minus -d (S i)) v)) x0 H5 H9) H10)))) H8)))))) (drop_trans_le i d (le_S_n i d (le_S -(S i) d H)) c1 c2 h H0 x H3))))) H2)))))))))))). -(* COMMENTS -Initial nodes: 627 -END *) +d (S i)) v)) x0 H5 H9) H10)))) H8)))))) (drop_trans_le i d (le_S_n i d +(le_S_n (S i) (S d) (le_S (S (S i)) (S d) (le_n_S (S i) d H)))) c1 c2 h H0 x +H3))))) H2)))))))))))). theorem drop_getl_trans_le: \forall (i: nat).(\forall (d: nat).((le i d) \to (\forall (c1: C).(\forall @@ -442,9 +420,6 @@ e2)))) (\lambda (x0: C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h O c1 e0))) (\lambda (e0: C).(\lambda (e1: C).(drop h (minus d i) e0 e1))) (\lambda (_: C).(\lambda (e1: C).(clear e1 e2))) x0 x H6 H7 H4)))) H5))))) H2)))))))))). -(* COMMENTS -Initial nodes: 323 -END *) theorem drop_getl_trans_ge: \forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall (d: @@ -458,9 +433,6 @@ C).(\lambda (H0: (getl i c2 e2)).(\lambda (H1: (le d i)).(let H2 \def (\lambda (e: C).(clear e e2)) (getl (plus i h) c1 e2) (\lambda (x: C).(\lambda (H3: (drop i O c2 x)).(\lambda (H4: (clear x e2)).(getl_intro (plus i h) c1 e2 x (drop_trans_ge i c1 c2 d h H x H3 H1) H4)))) H2)))))))))). -(* COMMENTS -Initial nodes: 137 -END *) theorem getl_drop_trans: \forall (c1: C).(\forall (c2: C).(\forall (h: nat).((getl h c1 c2) \to @@ -508,7 +480,4 @@ n)) O (CHead c2 (Flat f) t) e2))))))).(\lambda (H0: (getl (S n) (CHead c2 (Flat f) t) c3)).(\lambda (e2: C).(\lambda (i: nat).(\lambda (H1: (drop (S i) O c3 e2)).(drop_drop (Flat f) (plus i (S n)) c2 e2 (IHc c3 (S n) (getl_gen_S (Flat f) c2 c3 t n H0) e2 i H1) t))))))) h))))) k)))) c1). -(* COMMENTS -Initial nodes: 953 -END *) diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/flt.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/flt.ma index 3d6c90f73..db8d7be14 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/flt.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/flt.ma @@ -14,54 +14,76 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/fwd.ma". +include "basic_1/getl/fwd.ma". -include "Basic-1/clear/props.ma". - -include "Basic-1/flt/props.ma". +include "basic_1/flt/props.ma". theorem getl_flt: \forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c (CHead e (Bind b) u)) \to (flt e u c (TLRef i))))))) \def - \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e: + \lambda (b: B).(\lambda (c: C).(let TMP_2 \def (\lambda (c0: C).(\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to -(flt e u c0 (TLRef i))))))) (\lambda (n: nat).(\lambda (e: C).(\lambda (u: -T).(\lambda (i: nat).(\lambda (H: (getl i (CSort n) (CHead e (Bind b) -u))).(getl_gen_sort n i (CHead e (Bind b) u) H (flt e u (CSort n) (TLRef -i)))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u: -T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to (flt e u c0 (TLRef -i)))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e: C).(\lambda (u: -T).(\lambda (i: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t) -(CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) (\lambda (H0: -(getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear -(CHead c0 k0 t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef -O)))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e -(Bind b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 in C -return (\lambda (_: C).C) with [(CSort _) \Rightarrow e | (CHead c1 _ _) -\Rightarrow c1])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind -b0 c0 (CHead e (Bind b) u) t H1)) in ((let H3 \def (f_equal C B (\lambda (e0: -C).(match e0 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | -(CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with -[(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) -(CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in -((let H4 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda -(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) -(CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e -(Bind b) u) t H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e -c0)).(eq_ind_r T t (\lambda (t0: T).(flt e t0 (CHead c0 (Bind b0) t) (TLRef -O))) (eq_ind_r C c0 (\lambda (c1: C).(flt c1 t (CHead c0 (Bind b0) t) (TLRef -O))) (eq_ind B b (\lambda (b1: B).(flt c0 t (CHead c0 (Bind b1) t) (TLRef -O))) (flt_arith0 (Bind b) c0 t O) b0 H5) e H6) u H4)))) H3)) H2)))) (\lambda -(f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) -u))).(flt_arith1 (Bind b) e c0 u (clear_cle c0 (CHead e (Bind b) u) -(clear_gen_flat f c0 (CHead e (Bind b) u) t H1)) (Flat f) t O))) k -(getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n: -nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u -(CHead c0 k t) (TLRef n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead -e (Bind b) u))).(let H_y \def (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind -b) u) t n H1)) in (flt_arith2 e c0 u (r k n) H_y k t (S n)))))) i)))))))) c)). -(* COMMENTS -Initial nodes: 815 -END *) +(let TMP_1 \def (TLRef i) in (flt e u c0 TMP_1))))))) in (let TMP_8 \def +(\lambda (n: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (i: nat).(\lambda +(H: (getl i (CSort n) (CHead e (Bind b) u))).(let TMP_3 \def (Bind b) in (let +TMP_4 \def (CHead e TMP_3 u) in (let TMP_5 \def (CSort n) in (let TMP_6 \def +(TLRef i) in (let TMP_7 \def (flt e u TMP_5 TMP_6) in (getl_gen_sort n i +TMP_4 H TMP_7))))))))))) in (let TMP_79 \def (\lambda (c0: C).(\lambda (H: +((\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind +b) u)) \to (flt e u c0 (TLRef i)))))))).(\lambda (k: K).(\lambda (t: +T).(\lambda (e: C).(\lambda (u: T).(\lambda (i: nat).(let TMP_11 \def +(\lambda (n: nat).((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (let +TMP_9 \def (CHead c0 k t) in (let TMP_10 \def (TLRef n) in (flt e u TMP_9 +TMP_10))))) in (let TMP_71 \def (\lambda (H0: (getl O (CHead c0 k t) (CHead e +(Bind b) u))).(let TMP_14 \def (\lambda (k0: K).((clear (CHead c0 k0 t) +(CHead e (Bind b) u)) \to (let TMP_12 \def (CHead c0 k0 t) in (let TMP_13 +\def (TLRef O) in (flt e u TMP_12 TMP_13))))) in (let TMP_57 \def (\lambda +(b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e (Bind b) +u))).(let TMP_15 \def (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow +e | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_16 \def (Bind b) in (let +TMP_17 \def (CHead e TMP_16 u) in (let TMP_18 \def (Bind b0) in (let TMP_19 +\def (CHead c0 TMP_18 t) in (let TMP_20 \def (Bind b) in (let TMP_21 \def +(CHead e TMP_20 u) in (let TMP_22 \def (clear_gen_bind b0 c0 TMP_21 t H1) in +(let H2 \def (f_equal C C TMP_15 TMP_17 TMP_19 TMP_22) in (let TMP_23 \def +(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow b | (CHead _ k0 _) +\Rightarrow (match k0 with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow +b])])) in (let TMP_24 \def (Bind b) in (let TMP_25 \def (CHead e TMP_24 u) in +(let TMP_26 \def (Bind b0) in (let TMP_27 \def (CHead c0 TMP_26 t) in (let +TMP_28 \def (Bind b) in (let TMP_29 \def (CHead e TMP_28 u) in (let TMP_30 +\def (clear_gen_bind b0 c0 TMP_29 t H1) in (let H3 \def (f_equal C B TMP_23 +TMP_25 TMP_27 TMP_30) in (let TMP_31 \def (\lambda (e0: C).(match e0 with +[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_32 +\def (Bind b) in (let TMP_33 \def (CHead e TMP_32 u) in (let TMP_34 \def +(Bind b0) in (let TMP_35 \def (CHead c0 TMP_34 t) in (let TMP_36 \def (Bind +b) in (let TMP_37 \def (CHead e TMP_36 u) in (let TMP_38 \def (clear_gen_bind +b0 c0 TMP_37 t H1) in (let H4 \def (f_equal C T TMP_31 TMP_33 TMP_35 TMP_38) +in (let TMP_55 \def (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e +c0)).(let TMP_42 \def (\lambda (t0: T).(let TMP_39 \def (Bind b0) in (let +TMP_40 \def (CHead c0 TMP_39 t) in (let TMP_41 \def (TLRef O) in (flt e t0 +TMP_40 TMP_41))))) in (let TMP_46 \def (\lambda (c1: C).(let TMP_43 \def +(Bind b0) in (let TMP_44 \def (CHead c0 TMP_43 t) in (let TMP_45 \def (TLRef +O) in (flt c1 t TMP_44 TMP_45))))) in (let TMP_50 \def (\lambda (b1: B).(let +TMP_47 \def (Bind b1) in (let TMP_48 \def (CHead c0 TMP_47 t) in (let TMP_49 +\def (TLRef O) in (flt c0 t TMP_48 TMP_49))))) in (let TMP_51 \def (Bind b) +in (let TMP_52 \def (flt_arith0 TMP_51 c0 t O) in (let TMP_53 \def (eq_ind B +b TMP_50 TMP_52 b0 H5) in (let TMP_54 \def (eq_ind_r C c0 TMP_46 TMP_53 e H6) +in (eq_ind_r T t TMP_42 TMP_54 u H4)))))))))) in (let TMP_56 \def (TMP_55 H3) +in (TMP_56 H2)))))))))))))))))))))))))))))))) in (let TMP_66 \def (\lambda +(f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) u))).(let +TMP_58 \def (Bind b) in (let TMP_59 \def (Bind b) in (let TMP_60 \def (CHead +e TMP_59 u) in (let TMP_61 \def (Bind b) in (let TMP_62 \def (CHead e TMP_61 +u) in (let TMP_63 \def (clear_gen_flat f c0 TMP_62 t H1) in (let TMP_64 \def +(clear_cle c0 TMP_60 TMP_63) in (let TMP_65 \def (Flat f) in (flt_arith1 +TMP_58 e c0 u TMP_64 TMP_65 t O))))))))))) in (let TMP_67 \def (CHead c0 k t) +in (let TMP_68 \def (Bind b) in (let TMP_69 \def (CHead e TMP_68 u) in (let +TMP_70 \def (getl_gen_O TMP_67 TMP_69 H0) in (K_ind TMP_14 TMP_57 TMP_66 k +TMP_70))))))))) in (let TMP_78 \def (\lambda (n: nat).(\lambda (_: (((getl n +(CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef +n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead e (Bind b) u))).(let +TMP_72 \def (r k n) in (let TMP_73 \def (Bind b) in (let TMP_74 \def (CHead e +TMP_73 u) in (let TMP_75 \def (getl_gen_S k c0 TMP_74 t n H1) in (let H_y +\def (H e u TMP_72 TMP_75) in (let TMP_76 \def (r k n) in (let TMP_77 \def (S +n) in (flt_arith2 e c0 u TMP_76 H_y k t TMP_77))))))))))) in (nat_ind TMP_11 +TMP_71 TMP_78 i))))))))))) in (C_ind TMP_2 TMP_8 TMP_79 c))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma index b378f61fc..f8b2ebaa8 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma @@ -14,67 +14,78 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/defs.ma". +include "basic_1/getl/defs.ma". -include "Basic-1/drop/fwd.ma". +include "basic_1/drop/fwd.ma". -include "Basic-1/clear/fwd.ma". +include "basic_1/clear/fwd.ma". + +theorem getl_ind: + \forall (h: nat).(\forall (c1: C).(\forall (c2: C).(\forall (P: +Prop).(((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to P)))) \to +((getl h c1 c2) \to P))))) +\def + \lambda (h: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda (P: +Prop).(\lambda (f: ((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to +P))))).(\lambda (g: (getl h c1 c2)).(match g with [(getl_intro x x0 x1) +\Rightarrow (f x x0 x1)])))))). theorem getl_gen_all: \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e c2)))))) \def \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1 -c2)).(getl_ind i c1 c2 (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: -C).(clear e c2))) (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda -(H1: (clear e c2)).(ex_intro2 C (\lambda (e0: C).(drop i O c1 e0)) (\lambda -(e0: C).(clear e0 c2)) e H0 H1)))) H)))). -(* COMMENTS -Initial nodes: 95 -END *) +c2)).(let TMP_1 \def (\lambda (e: C).(drop i O c1 e)) in (let TMP_2 \def +(\lambda (e: C).(clear e c2)) in (let TMP_3 \def (ex2 C TMP_1 TMP_2) in (let +TMP_6 \def (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda (H1: +(clear e c2)).(let TMP_4 \def (\lambda (e0: C).(drop i O c1 e0)) in (let +TMP_5 \def (\lambda (e0: C).(clear e0 c2)) in (ex_intro2 C TMP_4 TMP_5 e H0 +H1)))))) in (getl_ind i c1 c2 TMP_3 TMP_6 H)))))))). theorem getl_gen_sort: \forall (n: nat).(\forall (h: nat).(\forall (x: C).((getl h (CSort n) x) \to (\forall (P: Prop).P)))) \def \lambda (n: nat).(\lambda (h: nat).(\lambda (x: C).(\lambda (H: (getl h -(CSort n) x)).(\lambda (P: Prop).(let H0 \def (getl_gen_all (CSort n) x h H) -in (ex2_ind C (\lambda (e: C).(drop h O (CSort n) e)) (\lambda (e: C).(clear -e x)) P (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) x0)).(\lambda (H2: -(clear x0 x)).(and3_ind (eq C x0 (CSort n)) (eq nat h O) (eq nat O O) P -(\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq nat h O)).(\lambda (_: -(eq nat O O)).(let H6 \def (eq_ind C x0 (\lambda (c: C).(clear c x)) H2 -(CSort n) H3) in (clear_gen_sort x n H6 P))))) (drop_gen_sort n h O x0 -H1))))) H0)))))). -(* COMMENTS -Initial nodes: 179 -END *) +(CSort n) x)).(\lambda (P: Prop).(let TMP_1 \def (CSort n) in (let H0 \def +(getl_gen_all TMP_1 x h H) in (let TMP_3 \def (\lambda (e: C).(let TMP_2 \def +(CSort n) in (drop h O TMP_2 e))) in (let TMP_4 \def (\lambda (e: C).(clear e +x)) in (let TMP_13 \def (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) +x0)).(\lambda (H2: (clear x0 x)).(let TMP_5 \def (CSort n) in (let TMP_6 \def +(eq C x0 TMP_5) in (let TMP_7 \def (eq nat h O) in (let TMP_8 \def (eq nat O +O) in (let TMP_11 \def (\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq +nat h O)).(\lambda (_: (eq nat O O)).(let TMP_9 \def (\lambda (c: C).(clear c +x)) in (let TMP_10 \def (CSort n) in (let H6 \def (eq_ind C x0 TMP_9 H2 +TMP_10 H3) in (clear_gen_sort x n H6 P))))))) in (let TMP_12 \def +(drop_gen_sort n h O x0 H1) in (and3_ind TMP_6 TMP_7 TMP_8 P TMP_11 +TMP_12)))))))))) in (ex2_ind C TMP_3 TMP_4 P TMP_13 H0)))))))))). theorem getl_gen_O: \forall (e: C).(\forall (x: C).((getl O e x) \to (clear e x))) \def \lambda (e: C).(\lambda (x: C).(\lambda (H: (getl O e x)).(let H0 \def -(getl_gen_all e x O H) in (ex2_ind C (\lambda (e0: C).(drop O O e e0)) -(\lambda (e0: C).(clear e0 x)) (clear e x) (\lambda (x0: C).(\lambda (H1: -(drop O O e x0)).(\lambda (H2: (clear x0 x)).(let H3 \def (eq_ind_r C x0 -(\lambda (c: C).(clear c x)) H2 e (drop_gen_refl e x0 H1)) in H3)))) H0)))). -(* COMMENTS -Initial nodes: 99 -END *) +(getl_gen_all e x O H) in (let TMP_1 \def (\lambda (e0: C).(drop O O e e0)) +in (let TMP_2 \def (\lambda (e0: C).(clear e0 x)) in (let TMP_3 \def (clear e +x) in (let TMP_6 \def (\lambda (x0: C).(\lambda (H1: (drop O O e +x0)).(\lambda (H2: (clear x0 x)).(let TMP_4 \def (\lambda (c: C).(clear c x)) +in (let TMP_5 \def (drop_gen_refl e x0 H1) in (let H3 \def (eq_ind_r C x0 +TMP_4 H2 e TMP_5) in H3)))))) in (ex2_ind C TMP_1 TMP_2 TMP_3 TMP_6 +H0)))))))). theorem getl_gen_S: \forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: nat).((getl (S h) (CHead c k u) x) \to (getl (r k h) c x)))))) \def \lambda (k: K).(\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h: -nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let H0 \def (getl_gen_all -(CHead c k u) x (S h) H) in (ex2_ind C (\lambda (e: C).(drop (S h) O (CHead c -k u) e)) (\lambda (e: C).(clear e x)) (getl (r k h) c x) (\lambda (x0: -C).(\lambda (H1: (drop (S h) O (CHead c k u) x0)).(\lambda (H2: (clear x0 -x)).(getl_intro (r k h) c x x0 (drop_gen_drop k c x0 u h H1) H2)))) H0))))))). -(* COMMENTS -Initial nodes: 145 -END *) +nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let TMP_1 \def (CHead c k u) +in (let TMP_2 \def (S h) in (let H0 \def (getl_gen_all TMP_1 x TMP_2 H) in +(let TMP_5 \def (\lambda (e: C).(let TMP_3 \def (S h) in (let TMP_4 \def +(CHead c k u) in (drop TMP_3 O TMP_4 e)))) in (let TMP_6 \def (\lambda (e: +C).(clear e x)) in (let TMP_7 \def (r k h) in (let TMP_8 \def (getl TMP_7 c +x) in (let TMP_11 \def (\lambda (x0: C).(\lambda (H1: (drop (S h) O (CHead c +k u) x0)).(\lambda (H2: (clear x0 x)).(let TMP_9 \def (r k h) in (let TMP_10 +\def (drop_gen_drop k c x0 u h H1) in (getl_intro TMP_9 c x x0 TMP_10 +H2)))))) in (ex2_ind C TMP_5 TMP_6 TMP_8 TMP_11 H0)))))))))))))). theorem getl_gen_2: \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex_3 @@ -82,39 +93,48 @@ B C T (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind b) v))))))))) \def \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1 -c2)).(let H0 \def (getl_gen_all c1 c2 i H) in (ex2_ind C (\lambda (e: -C).(drop i O c1 e)) (\lambda (e: C).(clear e c2)) (ex_3 B C T (\lambda (b: -B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind b) v)))))) -(\lambda (x: C).(\lambda (_: (drop i O c1 x)).(\lambda (H2: (clear x -c2)).(let H3 \def (clear_gen_all x c2 H2) in (ex_3_ind B C T (\lambda (b: -B).(\lambda (e: C).(\lambda (u: T).(eq C c2 (CHead e (Bind b) u))))) (ex_3 B -C T (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind -b) v)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4: -(eq C c2 (CHead x1 (Bind x0) x2))).(let H5 \def (eq_ind C c2 (\lambda (c: -C).(clear x c)) H2 (CHead x1 (Bind x0) x2) H4) in (eq_ind_r C (CHead x1 (Bind -x0) x2) (\lambda (c: C).(ex_3 B C T (\lambda (b: B).(\lambda (c0: C).(\lambda -(v: T).(eq C c (CHead c0 (Bind b) v))))))) (ex_3_intro B C T (\lambda (b: -B).(\lambda (c: C).(\lambda (v: T).(eq C (CHead x1 (Bind x0) x2) (CHead c -(Bind b) v))))) x0 x1 x2 (refl_equal C (CHead x1 (Bind x0) x2))) c2 H4)))))) -H3))))) H0))))). -(* COMMENTS -Initial nodes: 325 -END *) +c2)).(let H0 \def (getl_gen_all c1 c2 i H) in (let TMP_1 \def (\lambda (e: +C).(drop i O c1 e)) in (let TMP_2 \def (\lambda (e: C).(clear e c2)) in (let +TMP_5 \def (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(let TMP_3 \def +(Bind b) in (let TMP_4 \def (CHead c TMP_3 v) in (eq C c2 TMP_4)))))) in (let +TMP_6 \def (ex_3 B C T TMP_5) in (let TMP_33 \def (\lambda (x: C).(\lambda +(_: (drop i O c1 x)).(\lambda (H2: (clear x c2)).(let H3 \def (clear_gen_all +x c2 H2) in (let TMP_9 \def (\lambda (b: B).(\lambda (e: C).(\lambda (u: +T).(let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead e TMP_7 u) in (eq C c2 +TMP_8)))))) in (let TMP_12 \def (\lambda (b: B).(\lambda (c: C).(\lambda (v: +T).(let TMP_10 \def (Bind b) in (let TMP_11 \def (CHead c TMP_10 v) in (eq C +c2 TMP_11)))))) in (let TMP_13 \def (ex_3 B C T TMP_12) in (let TMP_32 \def +(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4: (eq C c2 +(CHead x1 (Bind x0) x2))).(let TMP_14 \def (\lambda (c: C).(clear x c)) in +(let TMP_15 \def (Bind x0) in (let TMP_16 \def (CHead x1 TMP_15 x2) in (let +H5 \def (eq_ind C c2 TMP_14 H2 TMP_16 H4) in (let TMP_17 \def (Bind x0) in +(let TMP_18 \def (CHead x1 TMP_17 x2) in (let TMP_22 \def (\lambda (c: +C).(let TMP_21 \def (\lambda (b: B).(\lambda (c0: C).(\lambda (v: T).(let +TMP_19 \def (Bind b) in (let TMP_20 \def (CHead c0 TMP_19 v) in (eq C c +TMP_20)))))) in (ex_3 B C T TMP_21))) in (let TMP_27 \def (\lambda (b: +B).(\lambda (c: C).(\lambda (v: T).(let TMP_23 \def (Bind x0) in (let TMP_24 +\def (CHead x1 TMP_23 x2) in (let TMP_25 \def (Bind b) in (let TMP_26 \def +(CHead c TMP_25 v) in (eq C TMP_24 TMP_26)))))))) in (let TMP_28 \def (Bind +x0) in (let TMP_29 \def (CHead x1 TMP_28 x2) in (let TMP_30 \def (refl_equal +C TMP_29) in (let TMP_31 \def (ex_3_intro B C T TMP_27 x0 x1 x2 TMP_30) in +(eq_ind_r C TMP_18 TMP_22 TMP_31 c2 H4))))))))))))))))) in (ex_3_ind B C T +TMP_9 TMP_13 TMP_32 H3))))))))) in (ex2_ind C TMP_1 TMP_2 TMP_6 TMP_33 +H0)))))))))). theorem getl_gen_flat: \forall (f: F).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: nat).((getl i (CHead e (Flat f) v) d) \to (getl i e d)))))) \def \lambda (f: F).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: -nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to (getl n -e d))) (\lambda (H: (getl O (CHead e (Flat f) v) d)).(getl_intro O e d e -(drop_refl e) (clear_gen_flat f e d v (getl_gen_O (CHead e (Flat f) v) d -H)))) (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Flat f) v) d) \to -(getl n e d)))).(\lambda (H0: (getl (S n) (CHead e (Flat f) v) -d)).(getl_gen_S (Flat f) e d v n H0)))) i))))). -(* COMMENTS -Initial nodes: 155 -END *) +nat).(let TMP_1 \def (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to +(getl n e d))) in (let TMP_7 \def (\lambda (H: (getl O (CHead e (Flat f) v) +d)).(let TMP_2 \def (drop_refl e) in (let TMP_3 \def (Flat f) in (let TMP_4 +\def (CHead e TMP_3 v) in (let TMP_5 \def (getl_gen_O TMP_4 d H) in (let +TMP_6 \def (clear_gen_flat f e d v TMP_5) in (getl_intro O e d e TMP_2 +TMP_6))))))) in (let TMP_9 \def (\lambda (n: nat).(\lambda (_: (((getl n +(CHead e (Flat f) v) d) \to (getl n e d)))).(\lambda (H0: (getl (S n) (CHead +e (Flat f) v) d)).(let TMP_8 \def (Flat f) in (getl_gen_S TMP_8 e d v n +H0))))) in (nat_ind TMP_1 TMP_7 TMP_9 i)))))))). theorem getl_gen_bind: \forall (b: B).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: @@ -123,26 +143,72 @@ nat).((getl i (CHead e (Bind b) v) d) \to (or (land (eq nat i O) (eq C d (j: nat).(getl j e d))))))))) \def \lambda (b: B).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: -nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to (or -(land (eq nat n O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: -nat).(eq nat n (S j))) (\lambda (j: nat).(getl j e d)))))) (\lambda (H: (getl -O (CHead e (Bind b) v) d)).(eq_ind_r C (CHead e (Bind b) v) (\lambda (c: -C).(or (land (eq nat O O) (eq C c (CHead e (Bind b) v))) (ex2 nat (\lambda -(j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e c))))) (or_introl -(land (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind b) v))) (ex2 nat -(\lambda (j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e (CHead e -(Bind b) v)))) (conj (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind -b) v)) (refl_equal nat O) (refl_equal C (CHead e (Bind b) v)))) d -(clear_gen_bind b e d v (getl_gen_O (CHead e (Bind b) v) d H)))) (\lambda (n: +nat).(let TMP_10 \def (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to +(let TMP_1 \def (eq nat n O) in (let TMP_2 \def (Bind b) in (let TMP_3 \def +(CHead e TMP_2 v) in (let TMP_4 \def (eq C d TMP_3) in (let TMP_5 \def (land +TMP_1 TMP_4) in (let TMP_7 \def (\lambda (j: nat).(let TMP_6 \def (S j) in +(eq nat n TMP_6))) in (let TMP_8 \def (\lambda (j: nat).(getl j e d)) in (let +TMP_9 \def (ex2 nat TMP_7 TMP_8) in (or TMP_5 TMP_9))))))))))) in (let TMP_52 +\def (\lambda (H: (getl O (CHead e (Bind b) v) d)).(let TMP_11 \def (Bind b) +in (let TMP_12 \def (CHead e TMP_11 v) in (let TMP_22 \def (\lambda (c: +C).(let TMP_13 \def (eq nat O O) in (let TMP_14 \def (Bind b) in (let TMP_15 +\def (CHead e TMP_14 v) in (let TMP_16 \def (eq C c TMP_15) in (let TMP_17 +\def (land TMP_13 TMP_16) in (let TMP_19 \def (\lambda (j: nat).(let TMP_18 +\def (S j) in (eq nat O TMP_18))) in (let TMP_20 \def (\lambda (j: nat).(getl +j e c)) in (let TMP_21 \def (ex2 nat TMP_19 TMP_20) in (or TMP_17 +TMP_21)))))))))) in (let TMP_23 \def (eq nat O O) in (let TMP_24 \def (Bind +b) in (let TMP_25 \def (CHead e TMP_24 v) in (let TMP_26 \def (Bind b) in +(let TMP_27 \def (CHead e TMP_26 v) in (let TMP_28 \def (eq C TMP_25 TMP_27) +in (let TMP_29 \def (land TMP_23 TMP_28) in (let TMP_31 \def (\lambda (j: +nat).(let TMP_30 \def (S j) in (eq nat O TMP_30))) in (let TMP_34 \def +(\lambda (j: nat).(let TMP_32 \def (Bind b) in (let TMP_33 \def (CHead e +TMP_32 v) in (getl j e TMP_33)))) in (let TMP_35 \def (ex2 nat TMP_31 TMP_34) +in (let TMP_36 \def (eq nat O O) in (let TMP_37 \def (Bind b) in (let TMP_38 +\def (CHead e TMP_37 v) in (let TMP_39 \def (Bind b) in (let TMP_40 \def +(CHead e TMP_39 v) in (let TMP_41 \def (eq C TMP_38 TMP_40) in (let TMP_42 +\def (refl_equal nat O) in (let TMP_43 \def (Bind b) in (let TMP_44 \def +(CHead e TMP_43 v) in (let TMP_45 \def (refl_equal C TMP_44) in (let TMP_46 +\def (conj TMP_36 TMP_41 TMP_42 TMP_45) in (let TMP_47 \def (or_introl TMP_29 +TMP_35 TMP_46) in (let TMP_48 \def (Bind b) in (let TMP_49 \def (CHead e +TMP_48 v) in (let TMP_50 \def (getl_gen_O TMP_49 d H) in (let TMP_51 \def +(clear_gen_bind b e d v TMP_50) in (eq_ind_r C TMP_12 TMP_22 TMP_47 d +TMP_51))))))))))))))))))))))))))))))) in (let TMP_73 \def (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Bind b) v) d) \to (or (land (eq nat n O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat n (S j))) (\lambda (j: nat).(getl j e d))))))).(\lambda (H0: (getl (S n) (CHead e -(Bind b) v) d)).(or_intror (land (eq nat (S n) O) (eq C d (CHead e (Bind b) -v))) (ex2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: nat).(getl -j e d))) (ex_intro2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: -nat).(getl j e d)) n (refl_equal nat (S n)) (getl_gen_S (Bind b) e d v n -H0)))))) i))))). -(* COMMENTS -Initial nodes: 525 -END *) +(Bind b) v) d)).(let TMP_53 \def (S n) in (let TMP_54 \def (eq nat TMP_53 O) +in (let TMP_55 \def (Bind b) in (let TMP_56 \def (CHead e TMP_55 v) in (let +TMP_57 \def (eq C d TMP_56) in (let TMP_58 \def (land TMP_54 TMP_57) in (let +TMP_61 \def (\lambda (j: nat).(let TMP_59 \def (S n) in (let TMP_60 \def (S +j) in (eq nat TMP_59 TMP_60)))) in (let TMP_62 \def (\lambda (j: nat).(getl j +e d)) in (let TMP_63 \def (ex2 nat TMP_61 TMP_62) in (let TMP_66 \def +(\lambda (j: nat).(let TMP_64 \def (S n) in (let TMP_65 \def (S j) in (eq nat +TMP_64 TMP_65)))) in (let TMP_67 \def (\lambda (j: nat).(getl j e d)) in (let +TMP_68 \def (S n) in (let TMP_69 \def (refl_equal nat TMP_68) in (let TMP_70 +\def (Bind b) in (let TMP_71 \def (getl_gen_S TMP_70 e d v n H0) in (let +TMP_72 \def (ex_intro2 nat TMP_66 TMP_67 n TMP_69 TMP_71) in (or_intror +TMP_58 TMP_63 TMP_72)))))))))))))))))))) in (nat_ind TMP_10 TMP_52 TMP_73 +i)))))))). + +theorem getl_mono: + \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to +(\forall (x2: C).((getl h c x2) \to (eq C x1 x2)))))) +\def + \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c +x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all +c x2 h H0) in (let TMP_1 \def (\lambda (e: C).(drop h O c e)) in (let TMP_2 +\def (\lambda (e: C).(clear e x2)) in (let TMP_3 \def (eq C x1 x2) in (let +TMP_14 \def (\lambda (x: C).(\lambda (H2: (drop h O c x)).(\lambda (H3: +(clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in (let TMP_4 \def +(\lambda (e: C).(drop h O c e)) in (let TMP_5 \def (\lambda (e: C).(clear e +x1)) in (let TMP_6 \def (eq C x1 x2) in (let TMP_13 \def (\lambda (x0: +C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear x0 x1)).(let TMP_7 +\def (\lambda (c0: C).(drop h O c c0)) in (let TMP_8 \def (drop_mono c x O h +H2 x0 H5) in (let H7 \def (eq_ind C x TMP_7 H2 x0 TMP_8) in (let TMP_9 \def +(\lambda (c0: C).(drop h O c c0)) in (let TMP_10 \def (drop_mono c x O h H2 +x0 H5) in (let H8 \def (eq_ind_r C x0 TMP_9 H7 x TMP_10) in (let TMP_11 \def +(\lambda (c0: C).(clear c0 x1)) in (let TMP_12 \def (drop_mono c x O h H2 x0 +H5) in (let H9 \def (eq_ind_r C x0 TMP_11 H6 x TMP_12) in (clear_mono x x1 H9 +x2 H3))))))))))))) in (ex2_ind C TMP_4 TMP_5 TMP_6 TMP_13 H4))))))))) in +(ex2_ind C TMP_1 TMP_2 TMP_3 TMP_14 H1))))))))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma index 71327becf..824b1b181 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/drop.ma". +include "basic_1/getl/drop.ma". -include "Basic-1/getl/clear.ma". +include "basic_1/getl/clear.ma". theorem getl_conf_le: \forall (i: nat).(\forall (a: C).(\forall (c: C).((getl i c a) \to (\forall @@ -25,14 +25,13 @@ a)))))))) \def \lambda (i: nat).(\lambda (a: C).(\lambda (c: C).(\lambda (H: (getl i c a)).(\lambda (e: C).(\lambda (h: nat).(\lambda (H0: (getl h c e)).(\lambda -(H1: (le h i)).(let H2 \def (getl_gen_all c e h H0) in (ex2_ind C (\lambda -(e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e)) (getl (minus i h) e -a) (\lambda (x: C).(\lambda (H3: (drop h O c x)).(\lambda (H4: (clear x -e)).(getl_clear_conf (minus i h) x a (getl_drop_conf_ge i a c H x h O H3 H1) -e H4)))) H2))))))))). -(* COMMENTS -Initial nodes: 133 -END *) +(H1: (le h i)).(let H2 \def (getl_gen_all c e h H0) in (let TMP_1 \def +(\lambda (e0: C).(drop h O c e0)) in (let TMP_2 \def (\lambda (e0: C).(clear +e0 e)) in (let TMP_3 \def (minus i h) in (let TMP_4 \def (getl TMP_3 e a) in +(let TMP_7 \def (\lambda (x: C).(\lambda (H3: (drop h O c x)).(\lambda (H4: +(clear x e)).(let TMP_5 \def (minus i h) in (let TMP_6 \def +(getl_drop_conf_ge i a c H x h O H3 H1) in (getl_clear_conf TMP_5 x a TMP_6 e +H4)))))) in (ex2_ind C TMP_1 TMP_2 TMP_4 TMP_7 H2)))))))))))))). theorem getl_trans: \forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall (h: nat).((getl @@ -41,17 +40,19 @@ e2))))))) \def \lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda (h: nat).(\lambda (H: (getl h c1 c2)).(\lambda (e2: C).(\lambda (H0: (getl i c2 -e2)).(let H1 \def (getl_gen_all c2 e2 i H0) in (ex2_ind C (\lambda (e: -C).(drop i O c2 e)) (\lambda (e: C).(clear e e2)) (getl (plus i h) c1 e2) -(\lambda (x: C).(\lambda (H2: (drop i O c2 x)).(\lambda (H3: (clear x -e2)).(nat_ind (\lambda (n: nat).((drop n O c2 x) \to (getl (plus n h) c1 -e2))) (\lambda (H4: (drop O O c2 x)).(let H5 \def (eq_ind_r C x (\lambda (c: -C).(clear c e2)) H3 c2 (drop_gen_refl c2 x H4)) in (getl_clear_trans (plus O -h) c1 c2 H e2 H5))) (\lambda (i0: nat).(\lambda (_: (((drop i0 O c2 x) \to -(getl (plus i0 h) c1 e2)))).(\lambda (H4: (drop (S i0) O c2 x)).(let H_y \def -(getl_drop_trans c1 c2 h H x i0 H4) in (getl_intro (plus (S i0) h) c1 e2 x -H_y H3))))) i H2)))) H1)))))))). -(* COMMENTS -Initial nodes: 247 -END *) +e2)).(let H1 \def (getl_gen_all c2 e2 i H0) in (let TMP_1 \def (\lambda (e: +C).(drop i O c2 e)) in (let TMP_2 \def (\lambda (e: C).(clear e e2)) in (let +TMP_3 \def (plus i h) in (let TMP_4 \def (getl TMP_3 c1 e2) in (let TMP_14 +\def (\lambda (x: C).(\lambda (H2: (drop i O c2 x)).(\lambda (H3: (clear x +e2)).(let TMP_6 \def (\lambda (n: nat).((drop n O c2 x) \to (let TMP_5 \def +(plus n h) in (getl TMP_5 c1 e2)))) in (let TMP_10 \def (\lambda (H4: (drop O +O c2 x)).(let TMP_7 \def (\lambda (c: C).(clear c e2)) in (let TMP_8 \def +(drop_gen_refl c2 x H4) in (let H5 \def (eq_ind_r C x TMP_7 H3 c2 TMP_8) in +(let TMP_9 \def (plus O h) in (getl_clear_trans TMP_9 c1 c2 H e2 H5)))))) in +(let TMP_13 \def (\lambda (i0: nat).(\lambda (_: (((drop i0 O c2 x) \to (getl +(plus i0 h) c1 e2)))).(\lambda (H4: (drop (S i0) O c2 x)).(let H_y \def +(getl_drop_trans c1 c2 h H x i0 H4) in (let TMP_11 \def (S i0) in (let TMP_12 +\def (plus TMP_11 h) in (getl_intro TMP_12 c1 e2 x H_y H3))))))) in (nat_ind +TMP_6 TMP_10 TMP_13 i H2))))))) in (ex2_ind C TMP_1 TMP_2 TMP_4 TMP_14 +H1))))))))))))). diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/props.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/props.ma index 9399ad4ab..2747e0c74 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/getl/props.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/getl/props.ma @@ -14,36 +14,37 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/getl/fwd.ma". +include "basic_1/getl/fwd.ma". -include "Basic-1/drop/props.ma". +include "basic_1/clear/props.ma". -include "Basic-1/clear/props.ma". +include "basic_1/drop/props.ma". theorem getl_refl: \forall (b: B).(\forall (c: C).(\forall (u: T).(getl O (CHead c (Bind b) u) (CHead c (Bind b) u)))) \def - \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(getl_intro O (CHead c (Bind -b) u) (CHead c (Bind b) u) (CHead c (Bind b) u) (drop_refl (CHead c (Bind b) -u)) (clear_bind b c u)))). -(* COMMENTS -Initial nodes: 59 -END *) + \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(let TMP_1 \def (Bind b) in +(let TMP_2 \def (CHead c TMP_1 u) in (let TMP_3 \def (Bind b) in (let TMP_4 +\def (CHead c TMP_3 u) in (let TMP_5 \def (Bind b) in (let TMP_6 \def (CHead +c TMP_5 u) in (let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead c TMP_7 u) +in (let TMP_9 \def (drop_refl TMP_8) in (let TMP_10 \def (clear_bind b c u) +in (getl_intro O TMP_2 TMP_4 TMP_6 TMP_9 TMP_10))))))))))))). theorem getl_head: \forall (k: K).(\forall (h: nat).(\forall (c: C).(\forall (e: C).((getl (r k h) c e) \to (\forall (u: T).(getl (S h) (CHead c k u) e)))))) \def \lambda (k: K).(\lambda (h: nat).(\lambda (c: C).(\lambda (e: C).(\lambda -(H: (getl (r k h) c e)).(\lambda (u: T).(let H0 \def (getl_gen_all c e (r k -h) H) in (ex2_ind C (\lambda (e0: C).(drop (r k h) O c e0)) (\lambda (e0: -C).(clear e0 e)) (getl (S h) (CHead c k u) e) (\lambda (x: C).(\lambda (H1: -(drop (r k h) O c x)).(\lambda (H2: (clear x e)).(getl_intro (S h) (CHead c k -u) e x (drop_drop k h c x H1 u) H2)))) H0))))))). -(* COMMENTS -Initial nodes: 137 -END *) +(H: (getl (r k h) c e)).(\lambda (u: T).(let TMP_1 \def (r k h) in (let H0 +\def (getl_gen_all c e TMP_1 H) in (let TMP_3 \def (\lambda (e0: C).(let +TMP_2 \def (r k h) in (drop TMP_2 O c e0))) in (let TMP_4 \def (\lambda (e0: +C).(clear e0 e)) in (let TMP_5 \def (S h) in (let TMP_6 \def (CHead c k u) in +(let TMP_7 \def (getl TMP_5 TMP_6 e) in (let TMP_11 \def (\lambda (x: +C).(\lambda (H1: (drop (r k h) O c x)).(\lambda (H2: (clear x e)).(let TMP_8 +\def (S h) in (let TMP_9 \def (CHead c k u) in (let TMP_10 \def (drop_drop k +h c x H1 u) in (getl_intro TMP_8 TMP_9 e x TMP_10 H2))))))) in (ex2_ind C +TMP_3 TMP_4 TMP_7 TMP_11 H0)))))))))))))). theorem getl_flat: \forall (c: C).(\forall (e: C).(\forall (h: nat).((getl h c e) \to (\forall @@ -51,19 +52,25 @@ theorem getl_flat: \def \lambda (c: C).(\lambda (e: C).(\lambda (h: nat).(\lambda (H: (getl h c e)).(\lambda (f: F).(\lambda (u: T).(let H0 \def (getl_gen_all c e h H) in -(ex2_ind C (\lambda (e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e)) -(getl h (CHead c (Flat f) u) e) (\lambda (x: C).(\lambda (H1: (drop h O c -x)).(\lambda (H2: (clear x e)).(nat_ind (\lambda (n: nat).((drop n O c x) \to -(getl n (CHead c (Flat f) u) e))) (\lambda (H3: (drop O O c x)).(let H4 \def -(eq_ind_r C x (\lambda (c0: C).(clear c0 e)) H2 c (drop_gen_refl c x H3)) in -(getl_intro O (CHead c (Flat f) u) e (CHead c (Flat f) u) (drop_refl (CHead c -(Flat f) u)) (clear_flat c e H4 f u)))) (\lambda (h0: nat).(\lambda (_: -(((drop h0 O c x) \to (getl h0 (CHead c (Flat f) u) e)))).(\lambda (H3: (drop -(S h0) O c x)).(getl_intro (S h0) (CHead c (Flat f) u) e x (drop_drop (Flat -f) h0 c x H3 u) H2)))) h H1)))) H0))))))). -(* COMMENTS -Initial nodes: 285 -END *) +(let TMP_1 \def (\lambda (e0: C).(drop h O c e0)) in (let TMP_2 \def (\lambda +(e0: C).(clear e0 e)) in (let TMP_3 \def (Flat f) in (let TMP_4 \def (CHead c +TMP_3 u) in (let TMP_5 \def (getl h TMP_4 e) in (let TMP_26 \def (\lambda (x: +C).(\lambda (H1: (drop h O c x)).(\lambda (H2: (clear x e)).(let TMP_8 \def +(\lambda (n: nat).((drop n O c x) \to (let TMP_6 \def (Flat f) in (let TMP_7 +\def (CHead c TMP_6 u) in (getl n TMP_7 e))))) in (let TMP_19 \def (\lambda +(H3: (drop O O c x)).(let TMP_9 \def (\lambda (c0: C).(clear c0 e)) in (let +TMP_10 \def (drop_gen_refl c x H3) in (let H4 \def (eq_ind_r C x TMP_9 H2 c +TMP_10) in (let TMP_11 \def (Flat f) in (let TMP_12 \def (CHead c TMP_11 u) +in (let TMP_13 \def (Flat f) in (let TMP_14 \def (CHead c TMP_13 u) in (let +TMP_15 \def (Flat f) in (let TMP_16 \def (CHead c TMP_15 u) in (let TMP_17 +\def (drop_refl TMP_16) in (let TMP_18 \def (clear_flat c e H4 f u) in +(getl_intro O TMP_12 e TMP_14 TMP_17 TMP_18))))))))))))) in (let TMP_25 \def +(\lambda (h0: nat).(\lambda (_: (((drop h0 O c x) \to (getl h0 (CHead c (Flat +f) u) e)))).(\lambda (H3: (drop (S h0) O c x)).(let TMP_20 \def (S h0) in +(let TMP_21 \def (Flat f) in (let TMP_22 \def (CHead c TMP_21 u) in (let +TMP_23 \def (Flat f) in (let TMP_24 \def (drop_drop TMP_23 h0 c x H3 u) in +(getl_intro TMP_20 TMP_22 e x TMP_24 H2))))))))) in (nat_ind TMP_8 TMP_19 +TMP_25 h H1))))))) in (ex2_ind C TMP_1 TMP_2 TMP_5 TMP_26 H0))))))))))))). theorem getl_ctail: \forall (b: B).(\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i: @@ -72,33 +79,17 @@ T).(getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u))))))))) \def \lambda (b: B).(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H: (getl i c (CHead d (Bind b) u))).(\lambda (k: K).(\lambda -(v: T).(let H0 \def (getl_gen_all c (CHead d (Bind b) u) i H) in (ex2_ind C -(\lambda (e: C).(drop i O c e)) (\lambda (e: C).(clear e (CHead d (Bind b) -u))) (getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)) (\lambda (x: -C).(\lambda (H1: (drop i O c x)).(\lambda (H2: (clear x (CHead d (Bind b) -u))).(getl_intro i (CTail k v c) (CHead (CTail k v d) (Bind b) u) (CTail k v -x) (drop_ctail c x O i H1 k v) (clear_ctail b x d u H2 k v))))) H0))))))))). -(* COMMENTS -Initial nodes: 203 -END *) - -theorem getl_mono: - \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to -(\forall (x2: C).((getl h c x2) \to (eq C x1 x2)))))) -\def - \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c -x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all -c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: -C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c -x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in -(ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq -C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear -x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0 -(drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0: -C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def -(eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0 -H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))). -(* COMMENTS -Initial nodes: 269 -END *) +(v: T).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead d TMP_1 u) in (let +H0 \def (getl_gen_all c TMP_2 i H) in (let TMP_3 \def (\lambda (e: C).(drop i +O c e)) in (let TMP_6 \def (\lambda (e: C).(let TMP_4 \def (Bind b) in (let +TMP_5 \def (CHead d TMP_4 u) in (clear e TMP_5)))) in (let TMP_7 \def (CTail +k v c) in (let TMP_8 \def (CTail k v d) in (let TMP_9 \def (Bind b) in (let +TMP_10 \def (CHead TMP_8 TMP_9 u) in (let TMP_11 \def (getl i TMP_7 TMP_10) +in (let TMP_19 \def (\lambda (x: C).(\lambda (H1: (drop i O c x)).(\lambda +(H2: (clear x (CHead d (Bind b) u))).(let TMP_12 \def (CTail k v c) in (let +TMP_13 \def (CTail k v d) in (let TMP_14 \def (Bind b) in (let TMP_15 \def +(CHead TMP_13 TMP_14 u) in (let TMP_16 \def (CTail k v x) in (let TMP_17 \def +(drop_ctail c x O i H1 k v) in (let TMP_18 \def (clear_ctail b x d u H2 k v) +in (getl_intro i TMP_12 TMP_15 TMP_16 TMP_17 TMP_18))))))))))) in (ex2_ind C +TMP_3 TMP_6 TMP_11 TMP_19 H0))))))))))))))))))). -- 2.39.2