- new extendedd beta-reductum involving native type annotation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / notation.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation.ma b/matita/matita/contribs/lambdadelta/basic_2/notation.ma
index 6a5b14e6213ff083f3f3965a7ba344d2dcb88cd2..140086abb50e6ff15d93387c6d1be1c930de6058 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/notation.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation.ma
@@ -116,10 +116,6 @@ notation "hvbox( T1 . break ⓛ T2 )"
  left associative with precedence 49
  for @{ 'DxAbst $T1 $T2 }.
 
-notation "hvbox( T . break ④ { term 46 I } break { term 46 T1 , break term 46 T2 , break term 46 T3 } )"
- non associative with precedence 50
- for @{ 'DxItem4 $T $I $T1 $T2 $T3 }.
-
 notation "hvbox( ♯ { term 46 x } )"
  non associative with precedence 90
  for @{ 'Weight $x }.
@@ -132,10 +128,6 @@ notation "hvbox( 𝐒 ⦃ term 46 T ⦄ )"
    non associative with precedence 45
    for @{ 'Simple $T }.
 
-notation "hvbox( L ⊢ break term 46 T1 ≈ break term 46 T2 )"
-   non associative with precedence 45
-   for @{ 'Hom $L $T1 $T2 }.
-
 notation "hvbox( T1 ≃ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'Iso $T1 $T2 }.
@@ -146,14 +138,6 @@ notation "hvbox( ⇧ [ term 46 d , break term 46 e ] break term 46 T1 ≡ break
    non associative with precedence 45
    for @{ 'RLift $d $e $T1 $T2 }.
 
-notation "hvbox( L1 break ⊑ [ term 46 d , break term 46 e ] break term 46 L2 )"
-   non associative with precedence 45
-   for @{ 'SubEq $L1 $d $e $L2 }.
-
-notation "hvbox( ⊒ [ term 46 d , break term 46 e ] break term 46 L2 )"
-   non associative with precedence 45
-   for @{ 'SubEqBottom $d $e $L2 }.
-
 notation "hvbox( ⇩ [ term 46 e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDrop $e $L1 $L2 }.
@@ -166,6 +150,14 @@ notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ⊃ break ⦃ term 46 L2 ,
    non associative with precedence 45
    for @{ 'SupTerm $L1 $T1 $L2 $T2 }.
 
+notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ⊃⸮ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'SupTermOpt $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ⊃⊃⸮ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'SupTermOptAlt $L1 $T1 $L2 $T2 }.
+
 notation "hvbox( L ⊢ break ⌘ ⦃ term 46 T ⦄ ≡ break term 46 k )"
    non associative with precedence 45
    for @{ 'ICM $L $T $k }.
@@ -196,6 +188,10 @@ notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ⊃ * break ⦃ term 46 L2
    non associative with precedence 45
    for @{ 'SupTermStar $L1 $T1 $L2 $T2 }.
 
+notation "hvbox( L1 ⊑ break term 46 L2 )"
+   non associative with precedence 45
+   for @{ 'CrSubEq $L1 $L2 }.
+
 notation "hvbox( L ⊢ break term 46 T1 ▶* break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PSubstStar $L $T1 $T2 }.
@@ -246,97 +242,103 @@ notation "hvbox( T1 ⊢ ➤ * break term 46 T2 )"
 
 (* Reduction ****************************************************************)
 
-notation "hvbox( L ⊢ break 𝐑 ⦃ term 46 T ⦄ )"
+notation "hvbox( L ⊢ 𝐑 break ⦃ term 46 T ⦄ )"
    non associative with precedence 45
    for @{ 'Reducible $L $T }.
 
-notation "hvbox( L ⊢ break 𝐈 ⦃ term 46 T ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ 𝐑 break [ term 46 g ] break ⦃ term 46 T ⦄ )"
+   non associative with precedence 45
+   for @{ 'Reducible $h $g $L $T }.
+
+notation "hvbox( L ⊢ 𝐈 break ⦃ term 46 T ⦄ )"
    non associative with precedence 45
    for @{ 'NotReducible $L $T }.
 
-notation "hvbox( L ⊢ break 𝐍 ⦃ term 46 T ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ 𝐈 break [ term 46 g ] break ⦃ term 46 T ⦄ )"
    non associative with precedence 45
-   for @{ 'Normal $L $T }.
+   for @{ 'NotReducible $h $g $L $T }.
 
-(* this might be removed *)
-notation "hvbox( 𝐇𝐑 ⦃ term 46 T ⦄ )"
+notation "hvbox( L ⊢ 𝐍 break ⦃ term 46 T ⦄ )"
    non associative with precedence 45
-   for @{ 'HdReducible $T }.
+   for @{ 'Normal $L $T }.
 
-(* this might be removed *)
-notation "hvbox( L ⊢ break 𝐇𝐑 ⦃ term 46 T ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ 𝐍 break [ term 46 g ] break ⦃ term 46 T ⦄ )"
    non associative with precedence 45
-   for @{ 'HdReducible $L $T }.
+   for @{ 'Normal $h $g $L $T }.
 
-(* this might be removed *)
-notation "hvbox( 𝐇𝐈 ⦃ term 46 T ⦄ )"
+notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'NotHdReducible $T }.
+   for @{ 'PRed $L $T1 $T2 }.
 
-(* this might be removed *)
-notation "hvbox( L ⊢ break 𝐇𝐈 ⦃ term 46 T ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ break term 46 T1 ➡ break [ term 46 g ] break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'NotHdReducible $L $T }.
+   for @{ 'PRed $h $g $L $T1 $T2 }.
 
-(* this might be removed *)
-notation "hvbox( 𝐇𝐍 ⦃ term 46 T ⦄ )"
+notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'HdNormal $T }.
+   for @{ 'PRedSn $L1 $L2 }.
 
-(* this might be removed *)
-notation "hvbox( L ⊢ break 𝐇𝐍 ⦃ term 46 T ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L1 ⦄ ⊢ ➡ break [ term 46 g ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'HdNormal $L $T }.
+   for @{ 'PRedSn $h $g $L1 $L2 }.
 
-notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
+(* Computation **************************************************************)
+
+notation "hvbox( ⦃ term 46 L, break term 46 T ⦄ ϵ break [ term 46 R ] break 〚term 46  A 〛 )"
    non associative with precedence 45
-   for @{ 'PRed $L $T1 $T2 }.
+   for @{ 'InEInt $R $L $T $A }.
 
-notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
+notation "hvbox( T1 ⊑ break [ term 46 R ] break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'PRedSn $L1 $L2 }.
+   for @{ 'CrSubEq $T1 $R $T2 }.
 
-(* Computation **************************************************************)
+notation "hvbox( L1 ⓝ ⊑ break term 46 L2 )"
+   non associative with precedence 45
+   for @{ 'CrSubEqT $L1 $L2 }.
 
 notation "hvbox( L ⊢ break term 46 T1 ➡ * break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRedStar $L $T1 $T2 }.
 
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ break term 46 T1 ➡ * break [ term 46 g ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PRedStar $h $g $L $T1 $T2 }.
+
 notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
    non associative with precedence 45
    for @{ 'PRedSnStar $L1 $L2 }.
 
-notation "hvbox( L ⊢ break term 46 T1 ➡ * break 𝐍 ⦃ term 46 T2 ⦄ )"
+notation "hvbox( ⦃ term 46 h, break term 46 L1 ⦄ ⊢ ➡ * break [ term 46 g ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'PEval $L $T1 $T2 }.
+   for @{ 'PRedSnStar $h $g $L1 $L2 }.
 
-notation "hvbox( ⬊ * term 46 T )"
+notation "hvbox( L1 ⊢ ➡ ➡ * break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'SN $T }.
+   for @{ 'PRedSnStarAlt $L1 $L2 }.
 
-notation "hvbox( L ⊢ ⬊ * break term 46 T )"
+notation "hvbox( ⦃ term 46 h, break term 46 L1 ⦄ ⊢ ➡ ➡ * break [ term 46 g ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'SN $L $T }.
+   for @{ 'PRedSnStarAlt $h $g $L1 $L2 }.
 
-notation "hvbox( L ⊢ ⬊ ⬊ * break term 46 T )"
+notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ break term 46 T1 • * ➡ * break [ term 46 g ] break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'SNAlt $L $T }.
+   for @{ 'DecomposedPRedStar $h $g $L $T1 $T2 }.
 
-notation "hvbox( ⦃ term 46 L, break term 46 T ⦄ ϵ break [ term 46 R ] break 〚term 46  A 〛 )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ ⬊ * break [ term 46 g ] break term 46 T )"
    non associative with precedence 45
-   for @{ 'InEInt $R $L $T $A }.
+   for @{ 'SN $h $g $L $T }.
 
-notation "hvbox( T1 ⊑ break [ term 46 R ] break term 46 T2 )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ ⬊ ⬊ * break [ term 46 g ] break term 46 T )"
    non associative with precedence 45
-   for @{ 'CrSubEq $T1 $R $T2 }.
+   for @{ 'SNAlt $h $g $L $T }.
 
-notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ break term 46 T1 • * ➡ * break [ term 46 g ] break term 46 T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ➡ * break 𝐍 ⦃ term 46 T2 ⦄ )"
    non associative with precedence 45
-   for @{ 'DecomposedXPRedStar $h $g $L $T1 $T2 }.
+   for @{ 'PEval $L $T1 $T2 }.
 
-notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ • * ⬊ * break [ term 46 g ] break term 46 T2 )"
+notation "hvbox( ⦃ term 46 h, break term 46 L ⦄ ⊢ break term 46 T1 ➡ * break [ term 46 g ] break 𝐍 ⦃ term 46 T2 ⦄ )"
    non associative with precedence 45
-   for @{ 'DecomposedXSN $h $g $L $T }.
+   for @{ 'PEval $h $g $L $T1 $T2 }.
 
 (* Conversion ***************************************************************)