λR. ∀U1,U2. R U1 U2 → ∀f,T1. ⬆*[f] T1 ≡ U1 →
∃∃T2. ⬆*[f] T2 ≡ U2 & R T1 T2.
+definition liftable2_bi: predicate (relation term) ≝
+ λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⬆*[f] T1 ≡ U1 →
+ ∀U2. ⬆*[f] T2 ≡ U2 → R U1 U2.
+
+definition deliftable2_bi: predicate (relation term) ≝
+ λR. ∀U1,U2. R U1 U2 → ∀f,T1. ⬆*[f] T1 ≡ U1 →
+ ∀T2. ⬆*[f] T2 ≡ U2 → R T1 T2.
+
(* Basic inversion lemmas ***************************************************)
fact lifts_inv_sort1_aux: ∀f,X,Y. ⬆*[f] X ≡ Y → ∀s. X = ⋆s → Y = ⋆s.
#f #T #U1 #H1 #U2 #H2 lapply (after_isid_sn 𝐈𝐝 … f)
/3 width=6 by lifts_conf, lifts_fwd_isid/
qed-.
+
+lemma liftable2_sn_bi: ∀R. liftable2 R → liftable2_bi R.
+#R #HR #T1 #T2 #HT12 #f #U1 #HTU1 #U2 #HTU2
+elim (HR … HT12 … HTU1) -HR -T1 #X #HTX #HUX
+<(lifts_mono … HTX … HTU2) -T2 -U2 -f //
+qed-.
+
+lemma deliftable2_sn_bi: ∀R. deliftable2_sn R → deliftable2_bi R.
+#R #HR #U1 #U2 #HU12 #f #T1 #HTU1 #T2 #HTU2
+elim (HR … HU12 … HTU1) -HR -U1 #X #HUX #HTX
+<(lifts_inj … HUX … HTU2) -U2 -T2 -f //
+qed-.
(**************************************************************************)
include "basic_2/syntax/tdeq.ma".
-include "basic_2/relocation/lifts.ma".
+include "basic_2/relocation/lifts_lifts.ma".
(* GENERIC RELOCATION FOR TERMS *********************************************)
]
qed-.
+lemma tdeq_lifts_bi: ∀h,o. liftable2_bi (tdeq h o).
+/3 width=6 by tdeq_lifts, liftable2_sn_bi/ qed-.
+
(* Inversion lemmas with degree-based equivalence for terms *****************)
lemma tdeq_inv_lifts: ∀h,o. deliftable2_sn (tdeq h o).
/3 width=5 by lifts_flat, tdeq_pair, ex2_intro/
]
qed-.
+
+lemma tdeq_inv_lifts_bi: ∀h,o. deliftable2_bi (tdeq h o).
+/3 width=6 by tdeq_inv_lifts, deliftable2_sn_bi/ qed-.
include "basic_2/syntax/tdeq_tdeq.ma".
include "basic_2/rt_transition/lfpx_lfdeq.ma".
-include "basic_2/rt_computation/csx.ma".
+include "basic_2/rt_computation/csx_drops.ma".
(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
|*: /3 width=3 by csx_cpx_trans/
]
qed.
+
+(* Basic_1: was just: sn3_abbr *)
+(* Basic_2A1: was: csx_lref_bind *)
+lemma csx_lref_drops: ∀h,o,I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V →
+ ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃#i⦄.
+#h #o #I #G #L #K #V #i #HLK #HV
+@csx_intro #X #H #Hi elim (cpx_inv_lref1_drops … H) -H
+[ #H destruct elim Hi //
+| -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
+ lapply (drops_mono … HLK0 … HLK) -HLK #H destruct
+ /3 width=8 by csx_lifts, csx_cpx_trans, drops_isuni_fwd_drop2/
+]
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was: sn3_gen_def *)
+(* Basic_2A1: was: csx_inv_lref_bind *)
+lemma csx_inv_lref_drops: ∀h,o,I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V →
+ ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃#i⦄ → ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
+#h #o #I #G #L #K #V #i #HLK #Hi
+elim (lifts_total V (𝐔❴⫯i❵))
+/4 width=9 by csx_inv_lifts, csx_cpx_trans, cpx_delta_drops, drops_isuni_fwd_drop2/
+qed-.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/relocation/lifts_tdeq.ma".
+include "basic_2/rt_transition/cpx_drops.ma".
+include "basic_2/rt_computation/csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with generic relocation ***************************************)
+
+(* Basic_1: was just: sn3_lift *)
+(* Basic_2A1: was just: csx_lift *)
+lemma csx_lifts: ∀h,o,G. d_liftable1 … (csx h o G).
+#h #o #G #K #T #H @(csx_ind … H) -T
+#T1 #_ #IH #b #f #L #HLK #U1 #HTU1
+@csx_intro #U2 #HU12 #HnU12
+elim (cpx_inv_lifts … HU12 … HLK … HTU1) -HU12
+/4 width=7 by tdeq_lifts_bi/
+qed-.
+
+(* Inversion lemmas with generic slicing ************************************)
+
+(* Basic_1: was just: sn3_gen_lift *)
+(* Basic_2A1: was just: csx_inv_lift *)
+lemma csx_inv_lifts: ∀h,o,G. d_deliftable1 … (csx h o G).
+#h #o #G #L #U #H @(csx_ind … H) -U
+#U1 #_ #IH #b #f #K #HLK #T1 #HTU1
+@csx_intro #T2 #HT12 #HnT12
+elim (cpx_lifts … HT12 … HLK … HTU1) -HT12
+/4 width=7 by tdeq_inv_lifts_bi/
+qed-.
--- /dev/null
+lemma csx_fqu_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ ⬈*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬈*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+/2 width=8 by csx_inv_lref_bind, csx_inv_lift, csx_fwd_flat_dx, csx_fwd_bind_dx, csx_fwd_pair_sn/
+qed-.
+
+lemma csx_fquq_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ ⬈*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬈*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fquq_inv_gen … H12) -H12
+[ /2 width=5 by csx_fqu_conf/
+| * #HG #HL #HT destruct //
+]
+qed-.
+
+lemma csx_fqup_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ ⬈*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬈*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/3 width=5 by csx_fqu_conf/
+qed-.
+
+lemma csx_fqus_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ ⬈*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬈*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fqus_inv_gen … H12) -H12
+[ /2 width=5 by csx_fqup_conf/
+| * #HG #HL #HT destruct //
+]
+qed-.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/static/gcp.ma".
+include "basic_2/rt_transition/cnx_drops.ma".
+include "basic_2/rt_computation/csx_drops.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Main properties **********************************************************)
+
+theorem csx_gcp: ∀h,o. gcp (cpx h) (tdeq h o) (csx h o).
+#h #o @mk_gcp
+[ normalize /3 width=13 by cnx_lifts/
+| #G #L elim (deg_total h o 0) /3 width=8 by cnx_sort_iter, ex_intro/
+| /2 width=8 by csx_lifts/
+| /2 width=3 by csx_fwd_flat_dx/
+]
+qed.
+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/reduction/cnx_lift.ma".
-include "basic_2/computation/gcp.ma".
-include "basic_2/computation/csx.ma".
-
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
-
-(* Relocation properties ****************************************************)
-
-(* Basic_1: was just: sn3_lift *)
-lemma csx_lift: ∀h,o,G,L2,L1,T1,b,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
- ∀T2. ⬇[b, l, k] L2 ≡ L1 → ⬆[l, k] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G #L2 #L1 #T1 #b #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
-@csx_intro #T #HLT2 #HT2
-elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
-@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_mono … HT0 … HT12) in HT2; -T1 /2 width=1 by/
-qed.
-
-(* Basic_1: was just: sn3_gen_lift *)
-lemma csx_inv_lift: ∀h,o,G,L2,L1,T1,b,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
- ∀T2. ⬇[b, l, k] L1 ≡ L2 → ⬆[l, k] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G #L2 #L1 #T1 #b #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
-@csx_intro #T #HLT2 #HT2
-elim (lift_total T l k) #T0 #HT0
-lapply (cpx_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
-@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_inj … HT0 … HT21) in HT2; -T1 /2 width=1 by/
-qed.
-
-(* Advanced inversion lemmas ************************************************)
-
-(* Basic_1: was: sn3_gen_def *)
-lemma csx_inv_lref_bind: ∀h,o,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V →
- ⦃G, L⦄ ⊢ ⬊*[h, o] #i → ⦃G, K⦄ ⊢ ⬊*[h, o] V.
-#h #o #I #G #L #K #V #i #HLK #Hi
-elim (lift_total V 0 (i+1))
-/4 width=9 by csx_inv_lift, csx_cpx_trans, cpx_delta, drop_fwd_drop2/
-qed-.
-
-(* Advanced properties ******************************************************)
-
-(* Basic_1: was just: sn3_abbr *)
-lemma csx_lref_bind: ∀h,o,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, o] V → ⦃G, L⦄ ⊢ ⬊*[h, o] #i.
-#h #o #I #G #L #K #V #i #HLK #HV
-@csx_intro #X #H #Hi
-elim (cpx_inv_lref1 … H) -H
-[ #H destruct elim Hi //
-| -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
- lapply (drop_mono … HLK0 … HLK) -HLK #H destruct
- /3 width=8 by csx_lift, csx_cpx_trans, drop_fwd_drop2/
-]
-qed.
-
-lemma csx_appl_simple: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬊*[h, o] V → ∀T1.
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T2) →
- 𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T1.
-#h #o #G #L #V #H @(csx_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
-@csx_intro #X #H1 #H2
-elim (cpx_inv_appl1_simple … H1) // -H1
-#V0 #T0 #HLV0 #HLT10 #H destruct
-elim (eq_false_inv_tpair_dx … H2) -H2
-[ -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/
-| -HLT10 * #H #HV0 destruct
- @IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto 17s *)
-]
-qed.
-
-lemma csx_fqu_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/2 width=8 by csx_inv_lref_bind, csx_inv_lift, csx_fwd_flat_dx, csx_fwd_bind_dx, csx_fwd_pair_sn/
-qed-.
-
-lemma csx_fquq_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fquq_inv_gen … H12) -H12
-[ /2 width=5 by csx_fqu_conf/
-| * #HG #HL #HT destruct //
-]
-qed-.
-
-lemma csx_fqup_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
-/3 width=5 by csx_fqu_conf/
-qed-.
-
-lemma csx_fqus_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fqus_inv_gen … H12) -H12
-[ /2 width=5 by csx_fqup_conf/
-| * #HG #HL #HT destruct //
-]
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem csx_gcp: ∀h,o. gcp (cpx h o) (eq …) (csx h o).
-#h #o @mk_gcp
-[ normalize /3 width=13 by cnx_lift/
-| #G #L elim (deg_total h o 0) /3 width=8 by cnx_sort_iter, ex_intro/
-| /2 width=8 by csx_lift/
-| /2 width=3 by csx_fwd_flat_dx/
-]
-qed.
lemma csx_appl_theta: ∀h,o,a,V1,V2. ⬆[0, 1] V1 ≡ V2 →
∀G,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, o] ⓓ{a}V.ⓐV2.T → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV1.ⓓ{a}V.T.
/2 width=5 by csx_appl_theta_aux/ qed.
-
-(* Basic_1: was just: sn3_appl_appl *)
-lemma csx_appl_simple_tsts: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬊*[h, o] V → ∀T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 ≂ T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T2) →
- 𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T1.
-#h #o #G #L #V #H @(csx_ind … H) -V #V #_ #IHV #T1 #H @(csx_ind … H) -T1 #T1 #H1T1 #IHT1 #H2T1 #H3T1
-@csx_intro #X #HL #H
-elim (cpx_inv_appl1_simple … HL) -HL //
-#V0 #T0 #HLV0 #HLT10 #H0 destruct
-elim (eq_false_inv_tpair_sn … H) -H
-[ -IHT1 #HV0
- @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
- @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
-| -IHV -H1T1 -HLV0 * #H #H1T10 destruct
- elim (tsts_dec T1 T0) #H2T10
- [ @IHT1 -IHT1 /4 width=3 by cpxs_strap2, cpxs_strap1, tsts_canc_sn, simple_tsts_repl_dx/
- | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
- ]
-]
-qed.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/rt_transition/cpx_simple.ma".
+include "basic_2/rt_computation/csx_csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with simple terms *********************************************)
+
+lemma csx_appl_simple: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ∀T1.
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T2⦄) →
+ 𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T1⦄.
+#h #o #G #L #V #H @(csx_ind … H) -V
+#V #_ #IHV #T1 #IHT1 #HT1
+@csx_intro #X #H1 #H2
+elim (cpx_inv_appl1_simple … H1) // -H1
+#V0 #T0 #HLV0 #HLT10 #H destruct
+elim (tdneq_inv_pair … H2) -H2
+[ #H elim H -H //
+| #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
+ @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
+| -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/
+]
+qed.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/syntax/tsts_simple.ma".
+include "basic_2/syntax/tsts_tsts.ma".
+include "basic_2/rt_transition/cpx_simple.ma".
+include "basic_2/rt_computation/cpxs.ma".
+include "basic_2/rt_computation/csx_csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with same top term structure **********************************)
+
+(* Basic_1: was just: sn3_appl_appl *)
+lemma csx_appl_simple_tsts: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T2⦄) →
+ 𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T1⦄.
+#h #o #G #L #V #H @(csx_ind … H) -V
+#V #_ #IHV #T1 #H @(csx_ind … H) -T1
+#T1 #H1T1 #IHT1 #H2T1 #H3T1
+@csx_intro #X #HL #H
+elim (cpx_inv_appl1_simple … HL) -HL //
+#V0 #T0 #HLV0 #HLT10 #H0 destruct
+elim (tdneq_inv_pair … H) -H
+[ #H elim H -H //
+| -IHT1 #HV0
+ @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
+ @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
+| -IHV -H1T1 #H1T10
+ @(csx_cpx_trans … (ⓐV.T0)) /2 width=1 by cpx_flat/ -HLV0
+ elim (tsts_dec h o T1 T0) #H2T10
+ [ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, tsts_canc_sn, simple_tsts_repl_dx/
+ | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
+ ]
+]
+qed.
cpxs.ma cpxs_tdeq.ma cpxs_tsts.ma cpxs_tsts_vector.ma cpxs_drops.ma cpxs_lsubr.ma cpxs_lfpx.ma cpxs_cnx.ma cpxs_cpxs.ma
lfpxs.ma lfpxs_fqup.ma lfpxs_cpxs.ma
-csx.ma csx_cnx.ma csx_cpxs.ma csx_csx.ma
+csx.ma csx_simple.ma csx_tsts.ma csx_drops.ma csx_gcp.ma csx_cnx.ma csx_cpxs.ma csx_csx.ma
csx_vector.ma
+++ /dev/null
-cpg.ma cpg_simple.ma cpg_drops.ma cpg_lsubr.ma
-cpx.ma cpx_simple.ma cpx_drops.ma cpx_fqus.ma cpx_lsubr.ma cpx_lfxs.ma cpx_lfdeq.ma
-lfpx.ma lfpx_length.ma lfpx_drops.ma lfpx_fqup.ma lfpx_frees.ma lfpx_lfdeq.ma lfpx_aaa.ma lfpx_lfpx.ma
-cnx.ma cnx_simple.ma cnx_drops.ma cnx_cnx.ma
-cpm.ma cpm_simple.ma cpm_drops.ma cpm_lsubr.ma cpm_lfxs.ma cpm_cpx.ma
-cpr.ma cpr_drops.ma
-lfpr.ma lfpr_length.ma lfpr_drops.ma lfpr_fquq.ma lfpr_fqup.ma lfpr_frees.ma lfpr_aaa.ma lfpr_lfpx.ma lfpr_lfpr.ma
-fpb.ma fpb_lfdeq.ma
-fpbq.ma fpbq_aaa.ma
[ "cpxs_lreq" + "cpxs_lleq" + "cpxs_aaa" * ]
*)
[ "csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" * ]
- [ "csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_cnx" + "csx_cpxs" + "csx_csx" * ]
+ [ "csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_tsts" + "csx_drops" + "csx_gcp" + "csx_cnx" + "csx_cpxs" + "csx_csx" * ]
[ "lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_fqup" + "lfpxs_cpxs" * ]
[ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_tsts" + "cpxs_tsts_vector" + "cpxs_drops" + "cpxs_lsubr" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ]
}
projects / helm.git / commitdiff