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4 (* ||A|| A project by Andrea Asperti *)
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15 include "delayed_updating/substitution/fsubst.ma".
16 include "delayed_updating/substitution/lift_prototerm.ma".
17 include "delayed_updating/syntax/prototerm_eq.ma".
18 include "delayed_updating/syntax/path_closed.ma".
19 include "delayed_updating/syntax/path_balanced.ma".
20 include "delayed_updating/syntax/path_structure.ma".
21 include "delayed_updating/notation/relations/black_rightarrow_ibf_3.ma".
22 include "ground/relocation/tr_uni.ma".
23 include "ground/arith/nat_rplus.ma".
24 include "ground/xoa/ex_6_5.ma".
26 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
28 definition ibfr (r): relation2 prototerm prototerm ≝
30 ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
31 ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓣ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
32 t1[⋔r←🠡[𝐮❨↑(m+n)❩](t1⋔(p◖𝗦))] ⇔ t2
36 "balanced focused reduction with immediate updating (prototerm)"
37 'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).
39 (* Constructions with subset_equivalence ************************************)
41 lemma ibfr_eq_trans (t) (t1) (t2) (r):
42 t1 ➡𝐢𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐢𝐛𝐟[r] t2.
44 * #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht #Ht2
45 /3 width=13 by subset_eq_trans, ex6_5_intro/