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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2A/multiple/mr2.ma".
17 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
19 (* Main properties **********************************************************)
21 theorem at_mono: ∀cs,i,i1. @⦃i, cs⦄ ≡ i1 → ∀i2. @⦃i, cs⦄ ≡ i2 → i1 = i2.
22 #cs #i #i1 #H elim H -cs -i -i1
23 [ #i #x #H <(at_inv_nil … H) -x //
24 | #cs #l #m #i #i1 #Hil #_ #IHi1 #x #H
25 lapply (at_inv_cons_lt … H Hil) -H -Hil /2 width=1 by/
26 | #cs #l #m #i #i1 #Hli #_ #IHi1 #x #H
27 lapply (at_inv_cons_ge … H Hli) -H -Hli /2 width=1 by/