i need to prove that if x is the first of sub([tex]\phi[/tex];a,[tex]\psi[/tex]) then there exists 1<=i<=n and there exist firsts [tex]\phi' of \phi_i and \psi' for \psi[/tex] such that x=sub([tex]\phi';a,\psi[/tex])[tex]\psi'[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where sub(t;a,b) is defined as follows:

let a1,..,an be n signs and b1,..,bn expressions.

a=(a1,...,an)

b=(b1,..,bn)

the substitution sub(t;a,b) is defined as:

if t is t1,...,tk then sub(t;a,b)=x1x2...xk

when 1<=i<=k xi is bj if ti=aj and xi is ti when ti isnt in {a1,...,an}.

what i did is as follows:

x is the first of sub(t;a,b) then there exists y such that sub(t;a,b)=xy

and let t' be the first of t, then t=t'z and thuse we can deduce that:

sub(t;a,b)=sub(t';a,b)sub(z;a,b)=xy

but i dont know how to procceed from here.

thanks in davance.

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# A question in substitution in logic.

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