include "basic_2/rt_transition/cpg_simple.ma".
include "basic_2/rt_transition/cpx.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS *****************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
-lemma cpx_inv_appl1_simple: ∀h,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[h] U → 𝐒⦃T1⦄ →
- ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ T1 ➡[h] T2 &
+(* Inversion lemmas with simple terms ***************************************)
+
+lemma cpx_inv_appl1_simple: ∀h,G,L,V1,T1,U. ⦃G,L⦄ ⊢ ⓐV1.T1 ⬈[h] U → 𝐒⦃T1⦄ →
+ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 & ⦃G,L⦄ ⊢ T1 ⬈[h] T2 &
U = ⓐV2.T2.
#h #G #L #V1 #T1 #U * #c #H #HT1 elim (cpg_inv_appl1_simple … H) -H
/3 width=5 by ex3_2_intro, ex_intro/