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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/unfold/lstas.ma".
16 include "basic_2/static/da_sta.ma".
18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
20 (* Properties on degree assignment for terms ********************************)
22 lemma lstas_da_conf: ∀h,g,G,L,T,U,l1. ⦃G, L⦄ ⊢ T •*[h, l1] U →
23 ∀l2. ⦃G, L⦄ ⊢ T ▪[h, g] l2 → ⦃G, L⦄ ⊢ U ▪[h, g] l2-l1.
24 #h #g #G #L #T #U #l1 #H @(lstas_ind_dx … H) -U -l1 //
25 #l1 #U #U0 #_ #HU0 #IHTU #l2 #HT
26 <minus_plus /3 width=3 by da_sta_conf/
29 (* Advanced inversion lemmas ************************************************)
31 lemma lstas_inv_refl_pos: ∀h,G,L,T,l. ⦃G, L⦄ ⊢ T •*[h, l+1] T → ⊥.
32 #h #G #L #T #l #H elim (lstas_inv_step_sn … H)
33 #U #HTU #_ elim (sta_da_ge … (l+1) HTU) -U
34 #g #l0 #HT #Hl0 lapply (lstas_da_conf … H … HT) -H
35 #H0T lapply (da_mono … HT … H0T) -h -G -L -T
36 #H elim (discr_x_minus_xy … H) -H
37 [ #H destruct /2 width=3 by le_plus_xSy_O_false/
38 | -Hl0 <plus_n_Sm #H destruct