(* Note: probably this is an inversion lemma *)
(* Basic_2A1: was: cpxs_fwd_delta *)
lemma cpxs_fwd_delta_drops (h) (I) (G) (L) (K):
- â\88\80V1,i. â¬\87*[i] L ≘ K.ⓑ{I}V1 →
- â\88\80V2. â¬\86*[↑i] V1 ≘ V2 →
+ â\88\80V1,i. â\87©*[i] L ≘ K.ⓑ{I}V1 →
+ â\88\80V2. â\87§*[↑i] V1 ≘ V2 →
∀X2. ⦃G,L⦄ ⊢ #i ⬈*[h] X2 →
∨∨ #i ⩳ X2 | ⦃G,L⦄ ⊢ V2 ⬈*[h] X2.
#h #I #G #L #K #V1 #i #HLK #V2 #HV12 #X2 #H
lemma cpxs_fwd_theta (h) (p) (G) (L):
∀V1,V,T,X2. ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] X2 →
- â\88\80V2. â¬\86*[1] V1 ≘ V2 →
+ â\88\80V2. â\87§*[1] V1 ≘ V2 →
∨∨ ⓐV1.ⓓ{p}V.T ⩳ X2 | ⦃G,L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] X2.
#h #p #G #L #V1 #V #T #X2 #H #V2 #HV12
elim (cpxs_inv_appl1 … H) -H *