# HG changeset patch
# User paulson
# Date 933094368 -7200
# Node ID 6f18ae72a90e66140e9541e188b631a90e15b761
# Parent  b2ee0e5d1a7fdd5c16285e7f65f2ee6c8b0dc86f
a new theory containing just an axiom needed to derive imp_cong

diff -r b2ee0e5d1a7f -r 6f18ae72a90e src/Sequents/LK.thy
--- a/src/Sequents/LK.thy	Tue Jul 27 18:52:23 1999 +0200
+++ b/src/Sequents/LK.thy	Tue Jul 27 18:52:48 1999 +0200
@@ -1,89 +1,19 @@
-(*  Title:      LK/lk.thy
+(*  Title:      LK/LK
     ID:         $Id$
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1993  University of Cambridge
 
-Classical First-Order Sequent Calculus
+Axiom to express monotonicity (a variant of the deduction theorem).  Makes the
+link between |- and ==>, needed for instance to prove imp_cong.
 
-There may be printing problems if a seqent is in expanded normal form
-	(eta-expanded, beta-contracted)
+CANNOT be added to LK0.thy because modal logic is built upon it, and
+various modal rules would become inconsistent.
 *)
 
-LK = Sequents +
-
-classes
-  term < logic
-
-default
-  term
-
-consts
-
- Trueprop	:: "two_seqi"
- "@Trueprop"	:: "two_seqe" ("((_)/ |- (_))" [6,6] 5)
-
-
-  True,False   :: o
-  "="          :: ['a,'a] => o       (infixl 50)
-  Not          :: o => o             ("~ _" [40] 40)
-  "&"          :: [o,o] => o         (infixr 35)
-  "|"          :: [o,o] => o         (infixr 30)
-  "-->","<->"  :: [o,o] => o         (infixr 25)
-  The          :: ('a => o) => 'a    (binder "THE " 10)
-  All          :: ('a => o) => o     (binder "ALL " 10)
-  Ex           :: ('a => o) => o     (binder "EX " 10)
+LK = LK0 +
 
 rules
-  (*Structural rules*)
-
-  basic "$H, P, $G |- $E, P, $F"
-
-  thinR "$H |- $E, $F ==> $H |- $E, P, $F"
-  thinL "$H, $G |- $E ==> $H, P, $G |- $E"
-
-  cut   "[| $H |- $E, P;  $H, P |- $E |] ==> $H |- $E"
-
-  (*Propositional rules*)
-
-  conjR "[| $H|- $E, P, $F;  $H|- $E, Q, $F |] ==> $H|- $E, P&Q, $F"
-  conjL "$H, P, Q, $G |- $E ==> $H, P & Q, $G |- $E"
-
-  disjR "$H |- $E, P, Q, $F ==> $H |- $E, P|Q, $F"
-  disjL "[| $H, P, $G |- $E;  $H, Q, $G |- $E |] ==> $H, P|Q, $G |- $E"
-
-  impR  "$H, P |- $E, Q, $F ==> $H |- $E, P-->Q, $F"
-  impL  "[| $H,$G |- $E,P;  $H, Q, $G |- $E |] ==> $H, P-->Q, $G |- $E"
-
-  notR  "$H, P |- $E, $F ==> $H |- $E, ~P, $F"
-  notL  "$H, $G |- $E, P ==> $H, ~P, $G |- $E"
-
-  FalseL "$H, False, $G |- $E"
 
-  True_def "True == False-->False"
-  iff_def  "P<->Q == (P-->Q) & (Q-->P)"
-
-  (*Quantifiers*)
-
-  allR  "(!!x.$H |- $E, P(x), $F) ==> $H |- $E, ALL x. P(x), $F"
-  allL  "$H, P(x), $G, ALL x. P(x) |- $E ==> $H, ALL x. P(x), $G |- $E"
-
-  exR   "$H |- $E, P(x), $F, EX x. P(x) ==> $H |- $E, EX x. P(x), $F"
-  exL   "(!!x.$H, P(x), $G |- $E) ==> $H, EX x. P(x), $G |- $E"
-
-  (*Equality*)
+  monotonic  "($H |- P ==> $H |- Q) ==> $H, P |- Q"
 
-  refl  "$H |- $E, a=a, $F"
-  sym   "$H |- $E, a=b, $F ==> $H |- $E, b=a, $F"
-  trans "[| $H|- $E, a=b, $F;  $H|- $E, b=c, $F |] ==> $H|- $E, a=c, $F"
-
-
-  (*Descriptions*)
-
-  The "[| $H |- $E, P(a), $F;  !!x.$H, P(x) |- $E, x=a, $F |] ==> 
-          $H |- $E, P(THE x. P(x)), $F"
 end
-
-  ML
-
-val parse_translation = [("@Trueprop",Sequents.two_seq_tr "Trueprop")];
-val print_translation = [("Trueprop",Sequents.two_seq_tr' "@Trueprop")];