turned translation for 1::nat into def.
introduced 1' and replaced most occurrences of 1 by 1'.
(* Title: HOLCF/porder.thy
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Conservative extension of theory Porder0 by constant definitions
*)
Porder = Porder0 +
consts
"<|" :: "['a set,'a::po] => bool" (infixl 55)
"<<|" :: "['a set,'a::po] => bool" (infixl 55)
lub :: "'a set => 'a::po"
is_tord :: "'a::po set => bool"
is_chain :: "(nat=>'a::po) => bool"
max_in_chain :: "[nat,nat=>'a::po]=>bool"
finite_chain :: "(nat=>'a::po)=>bool"
rules
(* class definitions *)
is_ub "S <| x == ! y.y:S --> y<<x"
is_lub "S <<| x == S <| x & (! u. S <| u --> x << u)"
lub "lub(S) = (@x. S <<| x)"
(* Arbitrary chains are total orders *)
is_tord "is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
(* Here we use countable chains and I prefer to code them as functions! *)
is_chain "is_chain(F) == (! i.F(i) << F(Suc(i)))"
(* finite chains, needed for monotony of continouous functions *)
max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)"
finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
end