1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/notation/relations/rdropstar_3.ma".
16 include "basic_2/notation/relations/rdropstar_4.ma".
17 include "basic_2/relocation/lreq.ma".
18 include "basic_2/relocation/lifts.ma".
20 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
22 (* Basic_1: includes: drop_skip_bind drop1_skip_bind *)
23 (* Basic_2A1: includes: drop_atom drop_pair drop_drop drop_skip
24 drop_refl_atom_O2 drop_drop_lt drop_skip_lt
26 inductive drops (b:bool): rtmap → relation lenv ≝
27 | drops_atom: ∀f. (b = Ⓣ → 𝐈⦃f⦄) → drops b (f) (⋆) (⋆)
28 | drops_drop: ∀f,I,L1,L2,V. drops b f L1 L2 → drops b (⫯f) (L1.ⓑ{I}V) L2
29 | drops_skip: ∀f,I,L1,L2,V1,V2.
30 drops b f L1 L2 → ⬆*[f] V2 ≡ V1 →
31 drops b (↑f) (L1.ⓑ{I}V1) (L2.ⓑ{I}V2)
34 interpretation "uniform slicing (local environment)"
35 'RDropStar i L1 L2 = (drops true (uni i) L1 L2).
37 interpretation "generic slicing (local environment)"
38 'RDropStar b f L1 L2 = (drops b f L1 L2).
40 definition d_liftable1: relation2 lenv term → predicate bool ≝
41 λR,b. ∀f,L,K. ⬇*[b, f] L ≡ K →
42 ∀T,U. ⬆*[f] T ≡ U → R K T → R L U.
44 definition d_liftable2: predicate (lenv → relation term) ≝
45 λR. ∀K,T1,T2. R K T1 T2 → ∀b,f,L. ⬇*[b, f] L ≡ K →
47 ∃∃U2. ⬆*[f] T2 ≡ U2 & R L U1 U2.
49 definition d_deliftable2_sn: predicate (lenv → relation term) ≝
50 λR. ∀L,U1,U2. R L U1 U2 → ∀b,f,K. ⬇*[b, f] L ≡ K →
52 ∃∃T2. ⬆*[f] T2 ≡ U2 & R K T1 T2.
54 definition dropable_sn: predicate (rtmap → relation lenv) ≝
55 λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 → ∀f2,L2. R f2 L1 L2 →
57 ∃∃K2. R f1 K1 K2 & ⬇*[b, f] L2 ≡ K2.
59 definition dropable_dx: predicate (rtmap → relation lenv) ≝
60 λR. ∀f2,L1,L2. R f2 L1 L2 →
61 ∀b,f,K2. ⬇*[b, f] L2 ≡ K2 → 𝐔⦃f⦄ →
63 ∃∃K1. ⬇*[b, f] L1 ≡ K1 & R f1 K1 K2.
65 definition dedropable_sn: predicate (rtmap → relation lenv) ≝
66 λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 → ∀f1,K2. R f1 K1 K2 →
68 ∃∃L2. R f2 L1 L2 & ⬇*[b, f] L2 ≡ K2 & L1 ≡[f] L2.
70 (* Basic properties *********************************************************)
72 lemma drops_eq_repl_back: ∀b,L1,L2. eq_repl_back … (λf. ⬇*[b, f] L1 ≡ L2).
73 #b #L1 #L2 #f1 #H elim H -f1 -L1 -L2
74 [ /4 width=3 by drops_atom, isid_eq_repl_back/
75 | #f1 #I #L1 #L2 #V #_ #IH #f2 #H elim (eq_inv_nx … H) -H
76 /3 width=3 by drops_drop/
77 | #f1 #I #L1 #L2 #V1 #v2 #_ #HV #IH #f2 #H elim (eq_inv_px … H) -H
78 /3 width=3 by drops_skip, lifts_eq_repl_back/
82 lemma drops_eq_repl_fwd: ∀b,L1,L2. eq_repl_fwd … (λf. ⬇*[b, f] L1 ≡ L2).
83 #b #L1 #L2 @eq_repl_sym /2 width=3 by drops_eq_repl_back/ (**) (* full auto fails *)
86 lemma drops_inv_tls_at: ∀f,i1,i2. @⦃i1,f⦄ ≡ i2 →
87 ∀b,L1,L2. ⬇*[b,⫱*[i2]f] L1 ≡ L2 →
88 ⬇*[b,↑⫱*[⫯i2]f] L1 ≡ L2.
89 /3 width=3 by drops_eq_repl_fwd, at_inv_tls/ qed-.
91 (* Basic_2A1: includes: drop_FT *)
92 lemma drops_TF: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≡ L2 → ⬇*[Ⓕ, f] L1 ≡ L2.
93 #f #L1 #L2 #H elim H -f -L1 -L2
94 /3 width=1 by drops_atom, drops_drop, drops_skip/
97 (* Basic_2A1: includes: drop_gen *)
98 lemma drops_gen: ∀b,f,L1,L2. ⬇*[Ⓣ, f] L1 ≡ L2 → ⬇*[b, f] L1 ≡ L2.
99 * /2 width=1 by drops_TF/
102 (* Basic_2A1: includes: drop_T *)
103 lemma drops_F: ∀b,f,L1,L2. ⬇*[b, f] L1 ≡ L2 → ⬇*[Ⓕ, f] L1 ≡ L2.
104 * /2 width=1 by drops_TF/
107 (* Basic_2A1: includes: drop_refl *)
108 lemma drops_refl: ∀b,L,f. 𝐈⦃f⦄ → ⬇*[b, f] L ≡ L.
109 #b #L elim L -L /2 width=1 by drops_atom/
110 #L #I #V #IHL #f #Hf elim (isid_inv_gen … Hf) -Hf
111 /3 width=1 by drops_skip, lifts_refl/
114 (* Basic_2A1: includes: drop_split *)
115 lemma drops_split_trans: ∀b,f,L1,L2. ⬇*[b, f] L1 ≡ L2 → ∀f1,f2. f1 ⊚ f2 ≡ f → 𝐔⦃f1⦄ →
116 ∃∃L. ⬇*[b, f1] L1 ≡ L & ⬇*[b, f2] L ≡ L2.
117 #b #f #L1 #L2 #H elim H -f -L1 -L2
118 [ #f #H0f #f1 #f2 #Hf #Hf1 @(ex2_intro … (⋆)) @drops_atom
120 #H elim (after_inv_isid3 … Hf H) -f //
121 | #f #I #L1 #L2 #V #HL12 #IHL12 #f1 #f2 #Hf #Hf1 elim (after_inv_xxn … Hf) -Hf [1,3: * |*: // ]
122 [ #g1 #g2 #Hf #H1 #H2 destruct
123 lapply (isuni_inv_push … Hf1 ??) -Hf1 [1,2: // ] #Hg1
125 /4 width=5 by drops_drop, drops_skip, lifts_refl, isuni_isid, ex2_intro/
126 | #g1 #Hf #H destruct elim (IHL12 … Hf) -f
127 /3 width=5 by ex2_intro, drops_drop, isuni_inv_next/
129 | #f #I #L1 #L2 #V1 #V2 #_ #HV21 #IHL12 #f1 #f2 #Hf #Hf1 elim (after_inv_xxp … Hf) -Hf [2,3: // ]
130 #g1 #g2 #Hf #H1 #H2 destruct elim (lifts_split_trans … HV21 … Hf) -HV21
131 elim (IHL12 … Hf) -f /3 width=5 by ex2_intro, drops_skip, isuni_fwd_push/
135 lemma drops_split_div: ∀b,f1,L1,L. ⬇*[b, f1] L1 ≡ L → ∀f2,f. f1 ⊚ f2 ≡ f → 𝐔⦃f2⦄ →
136 ∃∃L2. ⬇*[Ⓕ, f2] L ≡ L2 & ⬇*[Ⓕ, f] L1 ≡ L2.
137 #b #f1 #L1 #L #H elim H -f1 -L1 -L
138 [ #f1 #Hf1 #f2 #f #Hf #Hf2 @(ex2_intro … (⋆)) @drops_atom #H destruct
139 | #f1 #I #L1 #L #V #HL1 #IH #f2 #f #Hf #Hf2 elim (after_inv_nxx … Hf) -Hf [2,3: // ]
140 #g #Hg #H destruct elim (IH … Hg) -IH -Hg /3 width=5 by drops_drop, ex2_intro/
141 | #f1 #I #L1 #L #V1 #V #HL1 #HV1 #IH #f2 #f #Hf #Hf2
142 elim (after_inv_pxx … Hf) -Hf [1,3: * |*: // ]
143 #g2 #g #Hg #H2 #H0 destruct
144 [ lapply (isuni_inv_push … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -IH
145 lapply (after_isid_inv_dx … Hg … Hg2) -Hg #Hg
146 /5 width=7 by drops_eq_repl_back, drops_F, drops_refl, drops_skip, lifts_eq_repl_back, isid_push, ex2_intro/
147 | lapply (isuni_inv_next … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -HL1 -HV1
148 elim (IH … Hg) -f1 /3 width=3 by drops_drop, ex2_intro/
153 (* Basic forward lemmas *****************************************************)
155 (* Basic_1: includes: drop_gen_refl *)
156 (* Basic_2A1: includes: drop_inv_O2 *)
157 lemma drops_fwd_isid: ∀b,f,L1,L2. ⬇*[b, f] L1 ≡ L2 → 𝐈⦃f⦄ → L1 = L2.
158 #b #f #L1 #L2 #H elim H -f -L1 -L2 //
159 [ #f #I #L1 #L2 #V #_ #_ #H elim (isid_inv_next … H) //
160 | /5 width=5 by isid_inv_push, lifts_fwd_isid, eq_f3, sym_eq/
164 fact drops_fwd_drop2_aux: ∀b,f2,X,Y. ⬇*[b, f2] X ≡ Y → ∀I,K,V. Y = K.ⓑ{I}V →
165 ∃∃f1,f. 𝐈⦃f1⦄ & f2 ⊚ ⫯f1 ≡ f & ⬇*[b, f] X ≡ K.
166 #b #f2 #X #Y #H elim H -f2 -X -Y
167 [ #f2 #Hf2 #J #K #W #H destruct
168 | #f2 #I #L1 #L2 #V #_ #IHL #J #K #W #H elim (IHL … H) -IHL
169 /3 width=7 by after_next, ex3_2_intro, drops_drop/
170 | #f2 #I #L1 #L2 #V1 #V2 #HL #_ #_ #J #K #W #H destruct
171 lapply (isid_after_dx 𝐈𝐝 … f2) /3 width=9 by after_push, ex3_2_intro, drops_drop/
175 lemma drops_fwd_drop2: ∀b,f2,I,X,K,V. ⬇*[b, f2] X ≡ K.ⓑ{I}V →
176 ∃∃f1,f. 𝐈⦃f1⦄ & f2 ⊚ ⫯f1 ≡ f & ⬇*[b, f] X ≡ K.
177 /2 width=5 by drops_fwd_drop2_aux/ qed-.
179 lemma drops_after_fwd_drop2: ∀b,f2,I,X,K,V. ⬇*[b, f2] X ≡ K.ⓑ{I}V →
180 ∀f1,f. 𝐈⦃f1⦄ → f2 ⊚ ⫯f1 ≡ f → ⬇*[b, f] X ≡ K.
181 #b #f2 #I #X #K #V #H #f1 #f #Hf1 #Hf elim (drops_fwd_drop2 … H) -H
182 #g1 #g #Hg1 #Hg #HK lapply (after_mono_eq … Hg … Hf ??) -Hg -Hf
183 /3 width=5 by drops_eq_repl_back, isid_inv_eq_repl, eq_next/
186 (* Basic_1: was: drop_S *)
187 (* Basic_2A1: was: drop_fwd_drop2 *)
188 lemma drops_isuni_fwd_drop2: ∀b,f,I,X,K,V. 𝐔⦃f⦄ → ⬇*[b, f] X ≡ K.ⓑ{I}V → ⬇*[b, ⫯f] X ≡ K.
189 /3 width=7 by drops_after_fwd_drop2, after_isid_isuni/ qed-.
191 (* Forward lemmas with test for finite colength *****************************)
193 lemma drops_fwd_isfin: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≡ L2 → 𝐅⦃f⦄.
194 #f #L1 #L2 #H elim H -f -L1 -L2
195 /3 width=1 by isfin_next, isfin_push, isfin_isid/
198 (* Basic inversion lemmas ***************************************************)
200 fact drops_inv_atom1_aux: ∀b,f,X,Y. ⬇*[b, f] X ≡ Y → X = ⋆ →
201 Y = ⋆ ∧ (b = Ⓣ → 𝐈⦃f⦄).
202 #b #f #X #Y * -f -X -Y
203 [ /3 width=1 by conj/
204 | #f #I #L1 #L2 #V #_ #H destruct
205 | #f #I #L1 #L2 #V1 #V2 #_ #_ #H destruct
209 (* Basic_1: includes: drop_gen_sort *)
210 (* Basic_2A1: includes: drop_inv_atom1 *)
211 lemma drops_inv_atom1: ∀b,f,Y. ⬇*[b, f] ⋆ ≡ Y → Y = ⋆ ∧ (b = Ⓣ → 𝐈⦃f⦄).
212 /2 width=3 by drops_inv_atom1_aux/ qed-.
214 fact drops_inv_drop1_aux: ∀b,f,X,Y. ⬇*[b, f] X ≡ Y → ∀g,I,K,V. X = K.ⓑ{I}V → f = ⫯g →
216 #b #f #X #Y * -f -X -Y
217 [ #f #Hf #g #J #K #W #H destruct
218 | #f #I #L1 #L2 #V #HL #g #J #K #W #H1 #H2 <(injective_next … H2) -g destruct //
219 | #f #I #L1 #L2 #V1 #V2 #_ #_ #g #J #K #W #_ #H2 elim (discr_push_next … H2)
223 (* Basic_1: includes: drop_gen_drop *)
224 (* Basic_2A1: includes: drop_inv_drop1_lt drop_inv_drop1 *)
225 lemma drops_inv_drop1: ∀b,f,I,K,Y,V. ⬇*[b, ⫯f] K.ⓑ{I}V ≡ Y → ⬇*[b, f] K ≡ Y.
226 /2 width=7 by drops_inv_drop1_aux/ qed-.
228 fact drops_inv_skip1_aux: ∀b,f,X,Y. ⬇*[b, f] X ≡ Y → ∀g,I,K1,V1. X = K1.ⓑ{I}V1 → f = ↑g →
229 ∃∃K2,V2. ⬇*[b, g] K1 ≡ K2 & ⬆*[g] V2 ≡ V1 & Y = K2.ⓑ{I}V2.
230 #b #f #X #Y * -f -X -Y
231 [ #f #Hf #g #J #K1 #W1 #H destruct
232 | #f #I #L1 #L2 #V #_ #g #J #K1 #W1 #_ #H2 elim (discr_next_push … H2)
233 | #f #I #L1 #L2 #V1 #V2 #HL #HV #g #J #K1 #W1 #H1 #H2 <(injective_push … H2) -g destruct
234 /2 width=5 by ex3_2_intro/
238 (* Basic_1: includes: drop_gen_skip_l *)
239 (* Basic_2A1: includes: drop_inv_skip1 *)
240 lemma drops_inv_skip1: ∀b,f,I,K1,V1,Y. ⬇*[b, ↑f] K1.ⓑ{I}V1 ≡ Y →
241 ∃∃K2,V2. ⬇*[b, f] K1 ≡ K2 & ⬆*[f] V2 ≡ V1 & Y = K2.ⓑ{I}V2.
242 /2 width=5 by drops_inv_skip1_aux/ qed-.
244 fact drops_inv_skip2_aux: ∀b,f,X,Y. ⬇*[b, f] X ≡ Y → ∀g,I,K2,V2. Y = K2.ⓑ{I}V2 → f = ↑g →
245 ∃∃K1,V1. ⬇*[b, g] K1 ≡ K2 & ⬆*[g] V2 ≡ V1 & X = K1.ⓑ{I}V1.
246 #b #f #X #Y * -f -X -Y
247 [ #f #Hf #g #J #K2 #W2 #H destruct
248 | #f #I #L1 #L2 #V #_ #g #J #K2 #W2 #_ #H2 elim (discr_next_push … H2)
249 | #f #I #L1 #L2 #V1 #V2 #HL #HV #g #J #K2 #W2 #H1 #H2 <(injective_push … H2) -g destruct
250 /2 width=5 by ex3_2_intro/
254 (* Basic_1: includes: drop_gen_skip_r *)
255 (* Basic_2A1: includes: drop_inv_skip2 *)
256 lemma drops_inv_skip2: ∀b,f,I,X,K2,V2. ⬇*[b, ↑f] X ≡ K2.ⓑ{I}V2 →
257 ∃∃K1,V1. ⬇*[b, f] K1 ≡ K2 & ⬆*[f] V2 ≡ V1 & X = K1.ⓑ{I}V1.
258 /2 width=5 by drops_inv_skip2_aux/ qed-.
260 fact drops_inv_TF_aux: ∀f,L1,L2. ⬇*[Ⓕ, f] L1 ≡ L2 → 𝐔⦃f⦄ →
261 ∀I,K,V. L2 = K.ⓑ{I}V →
262 ⬇*[Ⓣ, f] L1 ≡ K.ⓑ{I}V.
263 #f #L1 #L2 #H elim H -f -L1 -L2
264 [ #f #_ #_ #J #K #W #H destruct
265 | #f #I #L1 #L2 #V #_ #IH #Hf #J #K #W #H destruct
266 /4 width=3 by drops_drop, isuni_inv_next/
267 | #f #I #L1 #L2 #V1 #V2 #HL12 #HV21 #_ #Hf #J #K #W #H destruct
268 lapply (isuni_inv_push … Hf ??) -Hf [1,2: // ] #Hf
269 <(drops_fwd_isid … HL12) -K // <(lifts_fwd_isid … HV21) -V1
270 /3 width=3 by drops_refl, isid_push/
274 (* Basic_2A1: includes: drop_inv_FT *)
275 lemma drops_inv_TF: ∀f,I,L,K,V. ⬇*[Ⓕ, f] L ≡ K.ⓑ{I}V → 𝐔⦃f⦄ →
276 ⬇*[Ⓣ, f] L ≡ K.ⓑ{I}V.
277 /2 width=3 by drops_inv_TF_aux/ qed-.
279 (* Advanced inversion lemmas ************************************************)
281 (* Basic_2A1: includes: drop_inv_gen *)
282 lemma drops_inv_gen: ∀b,f,I,L,K,V. ⬇*[b, f] L ≡ K.ⓑ{I}V → 𝐔⦃f⦄ →
283 ⬇*[Ⓣ, f] L ≡ K.ⓑ{I}V.
284 * /2 width=1 by drops_inv_TF/
287 (* Basic_2A1: includes: drop_inv_T *)
288 lemma drops_inv_F: ∀b,f,I,L,K,V. ⬇*[Ⓕ, f] L ≡ K.ⓑ{I}V → 𝐔⦃f⦄ →
289 ⬇*[b, f] L ≡ K.ⓑ{I}V.
290 * /2 width=1 by drops_inv_TF/
293 (* Inversion lemmas with test for uniformity ********************************)
295 lemma drops_inv_isuni: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≡ L2 → 𝐔⦃f⦄ →
297 ∃∃g,I,K,V. ⬇*[Ⓣ, g] K ≡ L2 & 𝐔⦃g⦄ & L1 = K.ⓑ{I}V & f = ⫯g.
298 #f #L1 #L2 * -f -L1 -L2
299 [ /4 width=1 by or_introl, conj/
300 | /4 width=8 by isuni_inv_next, ex4_4_intro, or_intror/
301 | /7 width=6 by drops_fwd_isid, lifts_fwd_isid, isuni_inv_push, isid_push, or_introl, conj, eq_f3, sym_eq/
305 (* Basic_2A1: was: drop_inv_O1_pair1 *)
306 lemma drops_inv_pair1_isuni: ∀b,f,I,K,L2,V. 𝐔⦃f⦄ → ⬇*[b, f] K.ⓑ{I}V ≡ L2 →
307 (𝐈⦃f⦄ ∧ L2 = K.ⓑ{I}V) ∨
308 ∃∃g. 𝐔⦃g⦄ & ⬇*[b, g] K ≡ L2 & f = ⫯g.
309 #b #f #I #K #L2 #V #Hf #H elim (isuni_split … Hf) -Hf * #g #Hg #H0 destruct
310 [ lapply (drops_inv_skip1 … H) -H * #Y #X #HY #HX #H destruct
311 <(drops_fwd_isid … HY Hg) -Y >(lifts_fwd_isid … HX Hg) -X
312 /4 width=3 by isid_push, or_introl, conj/
313 | lapply (drops_inv_drop1 … H) -H /3 width=4 by ex3_intro, or_intror/
317 (* Basic_2A1: was: drop_inv_O1_pair2 *)
318 lemma drops_inv_pair2_isuni: ∀b,f,I,K,V,L1. 𝐔⦃f⦄ → ⬇*[b, f] L1 ≡ K.ⓑ{I}V →
319 (𝐈⦃f⦄ ∧ L1 = K.ⓑ{I}V) ∨
320 ∃∃g,I1,K1,V1. 𝐔⦃g⦄ & ⬇*[b, g] K1 ≡ K.ⓑ{I}V & L1 = K1.ⓑ{I1}V1 & f = ⫯g.
322 [ #Hf #H elim (drops_inv_atom1 … H) -H #H destruct
323 | #L1 #I1 #V1 #Hf #H elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
324 [ #Hf #H destruct /3 width=1 by or_introl, conj/
325 | /3 width=8 by ex4_4_intro, or_intror/
330 lemma drops_inv_pair2_isuni_next: ∀b,f,I,K,V,L1. 𝐔⦃f⦄ → ⬇*[b, ⫯f] L1 ≡ K.ⓑ{I}V →
331 ∃∃I1,K1,V1. ⬇*[b, f] K1 ≡ K.ⓑ{I}V & L1 = K1.ⓑ{I1}V1.
332 #b #f #I #K #V #L1 #Hf #H elim (drops_inv_pair2_isuni … H) -H /2 width=3 by isuni_next/ -Hf *
333 [ #H elim (isid_inv_next … H) -H //
334 | /2 width=5 by ex2_3_intro/
338 (* Inversion lemmas with uniform relocations ********************************)
340 lemma drops_inv_succ: ∀l,L1,L2. ⬇*[⫯l] L1 ≡ L2 →
341 ∃∃I,K,V. ⬇*[l] K ≡ L2 & L1 = K.ⓑ{I}V.
342 #l #L1 #L2 #H elim (drops_inv_isuni … H) -H // *
343 [ #H elim (isid_inv_next … H) -H //
344 | /2 width=5 by ex2_3_intro/
348 (* Basic_2A1: removed theorems 12:
349 drops_inv_nil drops_inv_cons d1_liftable_liftables
350 drop_refl_atom_O2 drop_inv_pair1
351 drop_inv_Y1 drop_Y1 drop_O_Y drop_fwd_Y2
352 drop_fwd_length_minus2 drop_fwd_length_minus4
354 (* Basic_1: removed theorems 53:
355 drop1_gen_pnil drop1_gen_pcons drop1_getl_trans
356 drop_ctail drop_skip_flat
357 cimp_flat_sx cimp_flat_dx cimp_bind cimp_getl_conf
358 drop_clear drop_clear_O drop_clear_S
359 clear_gen_sort clear_gen_bind clear_gen_flat clear_gen_flat_r
360 clear_gen_all clear_clear clear_mono clear_trans clear_ctail clear_cle
361 getl_ctail_clen getl_gen_tail clear_getl_trans getl_clear_trans
362 getl_clear_bind getl_clear_conf getl_dec getl_drop getl_drop_conf_lt
363 getl_drop_conf_ge getl_conf_ge_drop getl_drop_conf_rev
364 drop_getl_trans_lt drop_getl_trans_le drop_getl_trans_ge
365 getl_drop_trans getl_flt getl_gen_all getl_gen_sort getl_gen_O
366 getl_gen_S getl_gen_2 getl_gen_flat getl_gen_bind getl_conf_le
367 getl_trans getl_refl getl_head getl_flat getl_ctail getl_mono