--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/notation/relations/black_rightarrow_ibf_3.ma".
+include "ground/relocation/tr_uni.ma".
+include "ground/arith/nat_rplus.ma".
+include "ground/xoa/ex_6_5.ma".
+
+(* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
+
+(**) (* explicit ninj because we cannot declare the expectd type of k *)
+definition ibfr (r): relation2 prototerm prototerm ≝
+ λt1,t2.
+ ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
+ ⊗b ϵ 𝐁 & b = ↳[h]b &
+ (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
+ t1[⋔r←↑[𝐮❨k+h❩](t1⋔(p◖𝗦))] ⇔ t2
+.
+
+interpretation
+ "balanced focused reduction with immediate updating (prototerm)"
+ 'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).