(* 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} →
- â\88¨â\88¨ â\88\83â\88\83K1. K1 â«\83 K2 & â¬\87*[b,f] L1 â\89\98 K1.â\93\98{I}
- | â\88\83â\88\83K1,W,V. K1 â«\83 K2 & â¬\87*[b,f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
- | â\88\83â\88\83J1,J2,K1,V. K1 â«\83 K2 & â¬\87*[b,f] L1 â\89\98 K1.â\93\91{J1}V & I = BUnit J2.
+ ∀L1,L2. L1 ⫃ L2 →
+ 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] →
+ â\88¨â\88¨ â\88\83â\88\83K1. K1 â«\83 K2 & â\87©*[b,f] L1 â\89\98 K1.â\93\98[I]
+ | â\88\83â\88\83K1,W,V. K1 â«\83 K2 & â\87©*[b,f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
+ | â\88\83â\88\83J1,J2,K1,V. K1 â«\83 K2 & â\87©*[b,f] L1 â\89\98 K1.â\93\91[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 â\86\92 â¬\87*[b,f] L2 ≘ K2.ⓓV →
- â\88\83â\88\83K1. K1 â«\83 K2 & â¬\87*[b,f] L1 ≘ K1.ⓓV.
+ â\88\80b,f,K2,V. ð\9d\90\94â\9dªfâ\9d« â\86\92 â\87©*[b,f] L2 ≘ K2.ⓓV →
+ â\88\83â\88\83K1. K1 â«\83 K2 & â\87©*[b,f] L1 ≘ K1.ⓓV.
#L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
elim (lsubr_fwd_drops2_bind … HL12 … Hf HLK2) -L2 -Hf // *
[ #K1 #W #V #_ #_ #H destruct