update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / ifr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 53853273b1ac2d004c120814cb7c718241381eee..765387b1c4243749c9687e883f52996660f2d879 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -12,20 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_balanced.ma".
 include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_preterm.ma".
-include "delayed_updating/notation/relations/black_rightarrow_f_4.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_reverse.ma".
+include "delayed_updating/notation/relations/black_rightarrow_if_4.ma".
 
 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
 
-inductive ifr (p) (q) (t): predicate preterm ≝
-| ifr_beta (b) (n):
-  let r ≝ p●𝗔◗b●𝗟◗q in
-  r◖𝗱❨n❩ ϵ t → ⊓⊗b → ifr p q t (t[⋔r←↑[𝐮❨n❩]t⋔(p◖𝗦)])
+definition ifr (p) (q): relation2 prototerm prototerm ≝
+           λt1,t2. ∃n:pnat.
+           let r ≝ p●𝗔◗𝗟◗q in
+           ∧∧ (𝗟◗q)ᴿ = ↳[n](𝗟◗q)ᴿ & r◖𝗱n ϵ t1 &
+              t1[⋔r←↑[𝐮❨n❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation
-  "focused balanced reduction with immediate updating (preterm)"
-  'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).
+  "focused reduction with immediate updating (prototerm)"
+  'BlackRightArrowIF t1 p q t2 = (ifr p q t1 t2).