Re: Help with a problem

On Fri, 25 Nov 2005 15:04:13 +0100, G. Frege <nomail@invalid> wrote:

>
> Informal proof:
>
> If r is positive, r is in E.
> Assume r is positive and r is in S.
> Then r is positive. Hence r is in E.
> With other words, if r is positive
> and r is in S, r is in E.
>
> The proof formalized in [one of] Gentzen's system[s] of ND:
>
> 1 (1) N -> O A
> 2 (2) N & P A
> 2 (3) N 2 &E
> 1,2 (4) O 1,3 MPP (->E)
> 1 (5) N & P -> O 2,4 CP (->I)
>

Actually, Gentzen would have written this proof the following way:

(2)
N & P
(1) ----- &E
N -> O N
------------------- ->E
O
---------- ->I(2)
N & P -> O


F.

--
"I do tend to feel Hughes & Cresswell is a more authoritative
source than you." (D. Ullrich)
.

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