EDB β€” 27Q

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Proposition 16

[27Q]Addition is associative.

Proof β–Ό

Consider

P(h)β‰βˆ€n,mβˆˆβ„•,(n+m)+h=n+(m+h);

Obviously P(0) is true, moreover P(Sh) is proven (omitting β€βˆ€n,mβˆˆβ„•β€) like this

(n+m)+Sh=S(n+m)+h=(Sn+m)+h=P(n)=Sn+(m+h)=n+S(m+h)=n+(m+Sh)\qedhere

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