(* Title: LK/LK
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Axiom to express monotonicity (a variant of the deduction theorem). Makes the
link between |- and ==>, needed for instance to prove imp_cong.
Axiom left_cong allows the simplifier to use left-side formulas. Ideally it
should be derived from lower-level axioms.
CANNOT be added to LK0.thy because modal logic is built upon it, and
various modal rules would become inconsistent.
*)
LK = LK0 +
rules
monotonic "($H |- P ==> $H |- Q) ==> $H, P |- Q"
left_cong "[| P == P'; |- P' ==> ($H |- $F) == ($H' |- $F') |]
==> (P, $H |- $F) == (P', $H' |- $F')"
end