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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/substitution/ldrop_ldrop.ma".
16 include "basic_2/static/aaa.ma".
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
20 (* Main properties **********************************************************)
22 theorem aaa_mono: ∀L,T,A1. L ⊢ T ⁝ A1 → ∀A2. L ⊢ T ⁝ A2 → A1 = A2.
23 #L #T #A1 #H elim H -L -T -A1
25 >(aaa_inv_sort … H) -H //
26 | #I1 #L #K1 #V1 #B #i #HLK1 #_ #IHA1 #A2 #H
27 elim (aaa_inv_lref … H) -H #I2 #K2 #V2 #HLK2 #HA2
28 lapply (ldrop_mono … HLK1 … HLK2) -L #H destruct /2 width=1/
29 | #a #L #V #T #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
30 elim (aaa_inv_abbr … H) -H /2 width=1/
31 | #a #L #V1 #T1 #B1 #A1 #_ #_ #IHB1 #IHA1 #X #H
32 elim (aaa_inv_abst … H) -H #B2 #A2 #HB2 #HA2 #H destruct /3 width=1/
33 | #L #V1 #T1 #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
34 elim (aaa_inv_appl … H) -H #B2 #_ #HA2
35 lapply (IHA1 … HA2) -L #H destruct //
36 | #L #V #T #A1 #_ #_ #_ #IHA1 #A2 #H
37 elim (aaa_inv_cast … H) -H /2 width=1/