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<b>let </b><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">z</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c2">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c4">z</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">z</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z</font> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:29"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c3">x</font>
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c4">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z</font></span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c2">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="arytm_2.html#T7" title="ARYTM_2:th.7">ARYTM_2:7</a></i>
<br/>.= 
<font color="Maroon" title="c4">z</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="txt" href="#E2:29"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="arytm_1.html#D1" target="_self" title="ARYTM_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z</font>
<b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="arytm_1.html#D1" target="_self" title="ARYTM_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c2">y</font>
<b>by </b><i><a class="ref" href="arytm_2.html#T7" title="ARYTM_2:th.7">ARYTM_2:7</a></i>
;<br/>
<b>hence </b><a NAME="E4:29"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">z</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z</font>
 <b>by </b><i><a class="ref" href="arytm_2.html#T12" title="ARYTM_2:th.12">ARYTM_2:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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