
Re: Two Finite Arithmetics
Posted:
Apr 8, 2014 2:08 PM


Here, I have translated your axioms into DC Proof format. Download my software, enter these axioms (the "@" is mapped to epsilon) and see what you can do with them. You have to construct your own proofs one line at a time, but the software will not let you make mistakes. Instant feedback is provided with each line you enter it. You might start by proving the associativity and commutativity of + and * as you have defined them. You can get started using with the tutorial or user manual.
Dan Download my DC Proof 2.0 software at http://www.dcproof.com Visit my new math blog at http://www.dcproof.wordpress.com
1 Set(n) Axiom
2 0 @ n Axiom
3 m @ n Axiom
4 ALL(a):[a @ n => s(a) @ n] Axiom
5 s(m)=m Axiom
6 ALL(a):~s(a)=0 Axiom
7 ALL(a):ALL(b):[a @ n & b @ n & ~a=m & ~b=m => [s(x)=s(y) => x=y]] Axiom
8 ALL(a):[Set(a) & ALL(b):[b @ a => b @ n] => [0 @ a & ALL(b):[b @ a => s(b) @ a] => ALL(b):[b @ n => b @ a]]] Axiom
9 ALL(a):ALL(b):[a @ n & b @ n => a+b @ n] Axiom
10 ALL(a):[a @ n => 0+a=a] Axiom
11 ALL(a):ALL(b):[a @ n & b @ n => s(a)+b=s(a+b)] Axiom
12 ALL(a):ALL(b):[a @ n & b @ n => a*b @ n] Axiom
13 ALL(a):[a @ n => 0*a=0] Axiom
14 ALL(a):[a @ n & b @ n => s(a)*b=a*b+b] Axiom

