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15 include "basic_2/rt_computation/lsubsx.ma".
17 (* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********)
19 (* Main properties **********************************************************)
21 theorem lsubsx_fix: ∀h,o,f,G,L1,L. G ⊢ L1 ⊆ⓧ[h, o, f] L →
22 ∀L2. G ⊢ L ⊆ⓧ[h, o, f] L2 → L = L2.
23 #h #o #f #G #L1 #L #H elim H -f -L1 -L
25 >(lsubsx_inv_atom_sn … H) -L2 //
26 | #f #I #K1 #K2 #_ #IH #L2 #H
27 elim (lsubsx_inv_push_sn … H) -H /3 width=1 by eq_f2/
28 | #f #I #K1 #K2 #_ #IH #L2 #H
29 elim (lsubsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
30 | #f #I #K1 #K2 #V #_ #_ #IH #L2 #H
31 elim (lsubsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
35 theorem lsubsx_trans: ∀h,o,f,G. Transitive … (lsubsx h o G f).
36 #h #o #f #G #L1 #L #H1 #L2 #H2
37 <(lsubsx_fix … H1 … H2) -L2 //