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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_1_1_1"/>
<font color="Maroon" title="c3">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c2">x</font>
 ;<br/><a NAME="E2:11_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">IT</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a>  st <font color="Maroon" title="c3">y</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Olive" title="b1">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="arytm_2.html#T10" title="ARYTM_2:th.10">ARYTM_2:10</a></i>;<br/><b>hence </b><a NAME="E3:11_1_1_1"/>
 ex <font color="Olive" title="b1">IT</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a>  st <font color="Olive" title="b1">IT</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:11_1_1"/>
( not <font color="Maroon" title="c3">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c2">x</font> implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  )
 <b>by </b><i><a class="ref" href="arytm_2.html#T21" title="ARYTM_2:th.21">ARYTM_2:21</a></i>;<br/>


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