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<b>thus </b><a NAME="E1:14_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="hilbert1.html#V4">with_propositional_variables</a> implies for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds  <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="hilbert1.html#D4">HILBERT1:def 4</a></i>;<br/>

<b>assume </b><a NAME="E2:14_2_1"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds  <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="hilbert1.html#D4">HILBERT1:def 4</a><br/>

<a NAME="E3:14_2_1"/>
 <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
;<br/>
<b>hence </b><a NAME="E4:14_2_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hilbert2.html#E2:14_2_1"><i><font color="Green">E9</font></i></a></i>;<br/>


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