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<span class="kw">let </span><font color="Maroon" title="c2">k</font>, <font color="Maroon" title="c3">k9</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c3">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> implies <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k9</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:4_1_2"/>
(  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c3">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k9</font></span><br/>

<a NAME="E2:4_1_2"/><span class="kw">then </span>
( 5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> &amp; 5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D2" onmouseover="rs('zf_lang/D2')" onmouseout="rh()">ZF_LANG:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:4_1_2"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T2" onmouseover="rs('xcmplx_1/T2')" onmouseout="rh()">XCMPLX_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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