(* Note: probably this is an inversion lemma *)
(* Basic_2A1: was: cpxs_fwd_delta *)
-lemma cpxs_fwd_delta_drops: â\88\80h,o,I,G,L,K,V1,i. â¬\87*[i] L â\89¡ K.ⓑ{I}V1 →
- â\88\80V2. â¬\86*[⫯i] V1 â\89¡ V2 →
+lemma cpxs_fwd_delta_drops: â\88\80h,o,I,G,L,K,V1,i. â¬\87*[i] L â\89\98 K.ⓑ{I}V1 →
+ â\88\80V2. â¬\86*[⫯i] V1 â\89\98 V2 →
∀U. ⦃G, L⦄ ⊢ #i ⬈*[h] U →
#i ⩳[h, o] U ∨ ⦃G, L⦄ ⊢ V2 ⬈*[h] U.
#h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
qed-.
lemma cpxs_fwd_theta: ∀h,o,p,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] U →
- â\88\80V2. â¬\86*[1] V1 â\89¡ V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
+ â\88\80V2. â¬\86*[1] V1 â\89\98 V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
⦃G, L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] U.
#h #o #p #G #L #V1 #V #T #U #H #V2 #HV12
elim (cpxs_inv_appl1 … H) -H *