qed.
lemma csx_applv_delta_drops (h) (G):
- â\88\80I,L,K,V1,i. â¬\87*[i] L ≘ K.ⓑ{I}V1 →
- â\88\80V2. â¬\86*[↑i] V1 ≘ V2 →
+ â\88\80I,L,K,V1,i. â\87©*[i] L ≘ K.ⓑ{I}V1 →
+ â\88\80V2. â\87§*[↑i] V1 ≘ V2 →
∀Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.V2⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.#i⦄.
#h #G #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
[ /4 width=11 by csx_inv_lifts, csx_lref_pair_drops, drops_isuni_fwd_drop2/
(* Basic_1: was just: sn3_appls_abbr *)
lemma csx_applv_theta (h) (G):
- â\88\80p,L,V1b,V2b. â¬\86*[1] V1b ≘ V2b →
+ â\88\80p,L,V1b,V2b. â\87§*[1] V1b ≘ V2b →
∀V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.ⒶV2b.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶV1b.ⓓ{p}V.T⦄.
#h #G #p #L #V1b #V2b * -V1b -V2b /2 width=1 by/
#V1b #V2b #V1 #V2 #HV12 #H