(* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
lemma lsubr_fwd_drops2_bind:
∀L1,L2. L1 ⫃ L2 →
- â\88\80b,f,I,K2. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\87©*[b,f] L2 â\89\98 K2.â\93\98{I} →
- ∨∨ ∃∃K1. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓘ{I}
+ â\88\80b,f,I,K2. ð\9d\90\94â\9dªfâ\9d« â\86\92 â\87©*[b,f] L2 â\89\98 K2.â\93\98[I] →
+ ∨∨ ∃∃K1. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓘ[I]
| ∃∃K1,W,V. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
- | ∃∃J1,J2,K1,V. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓑ{J1}V & I = BUnit J2.
+ | ∃∃J1,J2,K1,V. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓑ[J1]V & I = BUnit J2.
#L1 #L2 #H elim H -L1 -L2
[ #b #f #I #K2 #_ #H
elim (drops_inv_atom1 … H) -H #H destruct
(* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
lemma lsubr_fwd_drops2_abbr:
∀L1,L2. L1 ⫃ L2 →
- â\88\80b,f,K2,V. ð\9d\90\94â¦\83fâ¦\84 → ⇩*[b,f] L2 ≘ K2.ⓓV →
+ â\88\80b,f,K2,V. ð\9d\90\94â\9dªfâ\9d« → ⇩*[b,f] L2 ≘ K2.ⓓV →
∃∃K1. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓓV.
#L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
elim (lsubr_fwd_drops2_bind … HL12 … Hf HLK2) -L2 -Hf // *