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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/substitution/ldrop_ldrop.ma".
16 include "basic_2/static/ssta.ma".
18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
20 (* Main properties **********************************************************)
22 (* Note: apparently this was missing in basic_1 *)
23 theorem ssta_mono: ∀h,g,L,T,U1,l1. ⦃h, L⦄ ⊢ T •[g, l1] U1 →
24 ∀U2,l2. ⦃h, L⦄ ⊢ T •[g, l2] U2 → l1 = l2 ∧ U1 = U2.
25 #h #g #L #T #U1 #l1 #H elim H -L -T -U1 -l1
26 [ #L #k #l #Hkl #X #l2 #H
27 elim (ssta_inv_sort1 … H) -H #Hkl2 #H destruct
28 >(deg_mono … Hkl2 … Hkl) -g -L -l2 /2 width=1/
29 | #L #K #V #W #U1 #i #l1 #HLK #_ #HWU1 #IHVW #U2 #l2 #H
30 elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 [2: #l0] #HLK0 #HVW0 #HW0U2
31 lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
32 lapply (IHVW … HVW0) -IHVW -HVW0 * #H1 #H2 destruct
33 >(lift_mono … HWU1 … HW0U2) -W0 -U1 /2 width=1/
34 | #L #K #W #V #U1 #i #l1 #HLK #_ #HWU1 #IHWV #U2 #l2 #H
35 elim (ssta_inv_lref1 … H) -H * #K0 #W0 #V0 [2: #l0 ] #HLK0 #HWV0 #HV0U2
36 lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
37 lapply (IHWV … HWV0) -IHWV -HWV0 * #H1 #H2 destruct
38 >(lift_mono … HWU1 … HV0U2) -W -U1 /2 width=1/
39 | #a #I #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
40 elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct
41 elim (IHTU1 … HTU2) -T /3 width=1/
42 | #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
43 elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct
44 elim (IHTU1 … HTU2) -T /3 width=1/
45 | #L #V #W1 #T #U1 #l1 #_ #_ #IHVW1 #IHTU1 #U2 #l2 #H
46 elim (ssta_inv_cast1 … H) -H #W2 #T2 #HVW2 #HTU2 #H destruct
47 elim (IHVW1 … HVW2) -V
48 elim (IHTU1 … HTU2) -T /2 width=1/