src/ZF/ex/proplog.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/proplog.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,43 @@
+(*  Title: 	ZF/ex/prop-log.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow & Lawrence C Paulson
+    Copyright   1993  University of Cambridge
+
+Inductive definition of propositional logic.
+*)
+
+PropLog = Prop + Fin +
+consts
+  (*semantics*)
+  prop_rec :: "[i, i, i=>i, [i,i,i,i]=>i] => i"
+  is_true  :: "[i,i] => o"
+  "|="     :: "[i,i] => o"    			(infixl 50)
+  hyps     :: "[i,i] => i"
+
+  (*proof theory*)
+  thms     :: "i => i"
+  "|-"     :: "[i,i] => o"    			(infixl 50)
+
+translations
+  "H |- p" == "p : thms(H)"
+
+rules
+
+  prop_rec_def
+   "prop_rec(p,b,c,h) == \
+\   Vrec(p, %p g.prop_case(b, c, %x y. h(x, y, g`x, g`y), p))"
+
+  (** Semantics of propositional logic **)
+  is_true_def
+   "is_true(p,t) == prop_rec(p, 0,  %v. if(v:t, 1, 0), \
+\                               %p q tp tq. if(tp=1,tq,1))         =  1"
+
+  (*For every valuation, if all elements of H are true then so is p*)
+  sat_def     "H |= p == ALL t. (ALL q:H. is_true(q,t)) --> is_true(p,t)"
+
+  (** A finite set of hypotheses from t and the Vars in p **)
+  hyps_def
+   "hyps(p,t) == prop_rec(p, 0,  %v. {if(v:t, #v, #v=>Fls)}, \
+\                            %p q Hp Hq. Hp Un Hq)"
+
+end