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author | paulson |

Tue, 27 Jul 1999 18:52:48 +0200 | |

changeset 7094 | 6f18ae72a90e |

parent 7093 | b2ee0e5d1a7f |

child 7095 | cfc11af6174a |

a new theory containing just an axiom needed to derive imp_cong

--- 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")];