lemma lsubsv_fwd_lsuba: ∀h,g,G,L1,L2. G ⊢ L1 ⫃¡[h, g] L2 → G ⊢ L1 ⫃⁝ L2.
#h #g #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsuba_pair/
lemma lsubsv_fwd_lsuba: ∀h,g,G,L1,L2. G ⊢ L1 ⫃¡[h, g] L2 → G ⊢ L1 ⫃⁝ L2.
#h #g #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsuba_pair/
elim (snv_fwd_aaa … HW) -HW #B #HW
elim (snv_fwd_aaa … HV) -HV #A #HV
lapply (scpes_aaa_mono … HWV … HW … HV) #H destruct
elim (snv_fwd_aaa … HW) -HW #B #HW
elim (snv_fwd_aaa … HV) -HV #A #HV
lapply (scpes_aaa_mono … HWV … HW … HV) #H destruct