(* *)
(**************************************************************************)
-include "basic_2/syntax/theq_simple.ma".
-include "basic_2/syntax/theq_theq.ma".
+include "static_2/syntax/theq_simple.ma".
+include "static_2/syntax/theq_theq.ma".
include "basic_2/rt_transition/cpx_simple.ma".
include "basic_2/rt_computation/cpxs.ma".
include "basic_2/rt_computation/csx_csx.ma".
(* Basic_1: was just: sn3_appl_appl *)
(* Basic_2A1: was: csx_appl_simple_tsts *)
-lemma csx_appl_simple_theq: ∀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
+lemma csx_appl_simple_theq: ∀h,G,L,V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+ (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳ T2 → ⊥) → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T2⦄) →
+ 𝐒⦃T1⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T1⦄.
+#h #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
@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 (theq_dec h o T1 T0) #H2T10
+ elim (theq_dec T1 T0) #H2T10
[ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, theq_canc_sn, simple_theq_repl_dx/
| -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
]