old subst tactics removed. New destruct tactic used instead

[helm.git] / matita / contribs / LOGIC / PRed / defs.ma

diff --git a/matita/contribs/LOGIC/PRed/defs.ma b/matita/contribs/LOGIC/PRed/defs.ma
index 36b431098cf9d31f58c96a389d4b96778273f4e2..85a4c3bf9af0512e4ef7599cf0cdaeda1b00ac9b 100644 (file)
--- a/matita/contribs/LOGIC/PRed/defs.ma
+++ b/matita/contribs/LOGIC/PRed/defs.ma
@@ -18,22 +18,46 @@ set "baseuri" "cic:/matita/LOGIC/PRed/defs".
    For cut elimination 
 *)
 
-include "datatypes/Proof.ma".
-
-inductive PRed: Proof \to Proof \to Prop \def
-   | pred_lref: \forall i. PRed (lref i) (lref i)
-   | pred_parx: \forall h. PRed (parx h) (parx h)
-   | pred_impw: \forall p1,p2. PRed p1 p2 \to PRed (impw p1) (impw p2)
-   | pred_impr: \forall p1,p2. PRed p1 p2 \to PRed (impr p1) (impr p2)
-   | pred_impi: \forall p1,p2. PRed p1 p2 \to \forall q1,q2. PRed q1 q2 \to
-                \forall r1,r2. PRed r1 r2 \to 
-               PRed (impi p1 q1 r1) (impi p2 q2 r2)
-   | pred_scut: \forall p1,p2. PRed p1 p2 \to \forall q1,q2. PRed q1 q2 \to
-                PRed (scut p1 q1) (scut p2 q2)
+include "Insert/defs.ma".
+ 
+inductive PRed: Context \to Proof \to Sequent \to 
+                Context \to Proof \to Sequent \to Prop \def
+   | pred_lref: \forall P,i,S. PRed P (lref i) S P (lref i) S
+   | pred_prin: \forall P,h,S. PRed P (prin h) S P (prin h) S
+   | pred_impw: \forall Q1,Q2,p1,p2. (\forall S. PRed Q1 p1 S Q2 p2 S) \to 
+                \forall S. PRed Q1 (impw p1) S Q2 (impw p2) S
+   | pred_impr: \forall Q1,Q2,p1,p2. (\forall S. PRed Q1 p1 S Q2 p2 S) \to
+                \forall S. PRed Q1 (impr p1) S Q2 (impr p2) S
+   | pred_impi: \forall Q1,Q2,p1,p2. (\forall S. PRed Q1 p1 S Q2 p2 S) \to
+                \forall q1,q2. (\forall S. PRed Q1 q1 S Q2 q2 S) \to
+                \forall r1,r2. (\forall S,R. PRed (abst Q1 p1 q1 R) r1 S (abst Q2 p2 q2 R) r2 S) \to 
+                \forall S. PRed Q1 (impi p1 q1 r1) S Q2 (impi p2 q2 r2) S
+   | pred_scut: \forall Q1,Q2,p1,p2. (\forall S. PRed Q1 p1 S Q2 p2 S) \to 
+                \forall q1,q2. (\forall S. PRed Q1 q1 S Q2 q2 S) \to
+                \forall S. PRed Q1 (scut p1 q1) S Q2 (scut p2 q2) S
+   | pred_a_sx: \forall p1,p2,R,P,Q1,i. Insert p1 p2 R i P Q1 \to
+                \forall q0,S,Q2. Insert p1 (scut p2 q0) S i P Q2 \to
+                \forall q. Lift zero i q0 q \to
+               PRed Q1 (scut (lref i) q) S Q2 (lref i) S
+   | pred_a_dx: \forall q1,q2,R,P,Q1,i. Insert q1 q2 R i P Q1 \to
+                \forall p0,S,Q2. Insert (scut p0 q1) q2 S i P Q2 \to
+                \forall p. Lift zero i p0 p \to
+               PRed Q1 (scut p (lref i)) S Q2 (lref i) S
+   | pred_b_sx: \forall q1,q2,P1,P2,S. PRed P1 q1 S P2 q2 S \to 
+                \forall h. PRed P1 (scut (prin h) q1) S P2 q2 S
+   | pred_b_dx: \forall p1,p2,Q1,Q2,S. PRed Q1 p1 S Q2 p2 S \to
+                \forall h. PRed Q1 (scut p1 (prin h)) S Q2 p2 S
+   | pred_c   : \forall p1,p2,Q1,Q2,S. PRed Q1 p1 S Q2 p2 S \to 
+                \forall p. PRed Q1 (scut (impr p) (impw p1)) S Q2 p2 S    
 .
 
 (*CSC: the URI must disappear: there is a bug now *)
 interpretation 
    "single step parallel reduction in B->"
-   'parred x y = (cic:/matita/LOGIC/PRed/defs/PRed.ind#xpointer(1/1) x y)
+   'parred3 x1 y1 z1 x2 y2 z2 = 
+      (cic:/matita/LOGIC/PRed/defs/PRed.ind#xpointer(1/1) x1 y1 z1 x2 y2 z2)
 .
+
+notation "hvbox([a1,b1,c1] break => [a2,b2,c2])" 
+  non associative with precedence 45
+for @{ 'parred3 $a1 $b1 $c1 $a2 $b2 $c2 }.