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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/static/da_da.ma".
16 include "basic_2/static/ssta_lift.ma".
18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
20 (* Advanced inversion lemmas ************************************************)
22 lemma ssta_inv_refl_pos: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] T → ⊥.
23 #h #g #G #L #T #l #H1T #HTT
24 lapply (ssta_da_conf … HTT … H1T) -HTT <minus_plus_m_m #H2T
25 lapply (da_mono … H2T … H1T) -h -G -L -T #H
26 elim (plus_xySz_x_false 0 l 0) //
29 (* Main properties **********************************************************)
31 theorem ssta_mono: ∀h,g,G,L. singlevalued … (ssta h g G L).
32 #h #g #G #L #T #U1 #H elim H -G -L -T -U1
33 [ #G #L #k #X #H >(ssta_inv_sort1 … H) -X //
34 | #G #L #K #V #U1 #W #i #HLK #_ #HWU1 #IHVW #U2 #H
35 elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
36 lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
37 lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
38 >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
39 | #G #L #K #W #U1 #l #i #HLK #HWl #HWU1 #U2 #H
40 elim (ssta_inv_lref1 … H) -H * #K0 #W0 #l0 #HLK0 #HWl0 #HW0U2
41 lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
42 lapply (da_mono … HWl0 … HWl) -HWl0 #H destruct
43 >(lift_mono … HWU1 … HW0U2) -W -U1 //
44 | #a #I #G #L #V #T #U1 #_ #IHTU1 #X #H
45 elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
46 | #G #L #V #T #U1 #_ #IHTU1 #X #H
47 elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
48 | #G #L #W #T #U1 #_ #IHTU1 #U2 #H
49 lapply (ssta_inv_cast1 … H) -H /2 width=1/