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Proof by complete induction on termforallminN,ninN: (m!= 0 \/n!= 0) => Euclid(m,n) = gcd(m,n).

We take arbitrary `m` in **N** and `n` in **N** and assume

We have to prove

(1) forallxinN,yinN:x+y<m+n=>( x!= 0 \/y!= 0) => Euclid(x,y) = gcd(x,y).

We assume (3) (

(2) ( m!= 0 \/n!= 0) => Euclid(m,n) = gcd(m,n).

Author: Wolfgang Schreiner

Last Modification: November 24, 1999