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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
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8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2A/static/da_lift.ma".
16
17 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
18
19 (* Main properties **********************************************************)
20
21 theorem da_mono: ∀h,g,G,L,T,d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 →
22                  ∀d2. ⦃G, L⦄ ⊢ T ▪[h, g] d2 → d1 = d2.
23 #h #g #G #L #T #d1 #H elim H -G -L -T -d1
24 [ #G #L #k #d1 #Hkd1 #d2 #H
25   lapply (da_inv_sort … H) -G -L #Hkd2
26   >(deg_mono … Hkd2 … Hkd1) -h -k -d2 //
27 | #G #L #K #V #i #d1 #HLK #_ #IHV #d2 #H
28   elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 #HV0 [| #Hd0 ]
29   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /2 width=1 by/
30 | #G #L #K #W #i #d1 #HLK #_ #IHW #d2 #H
31   elim (da_inv_lref … H) -H * #K0 #W0 [| #d0 ] #HLK0 #HW0 [| #Hd0 ]
32   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /3 width=1 by eq_f/
33 | #a #I #G #L #V #T #d1 #_ #IHT #d2 #H
34   lapply (da_inv_bind … H) -H /2 width=1 by/
35 | #I #G #L #V #T #d1 #_ #IHT #d2 #H
36   lapply (da_inv_flat … H) -H /2 width=1 by/
37 ]
38 qed-.