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<span class="kw">set </span><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="valued_0.html#D11" onmouseover="rs('valued_0/D11')" onmouseout="rh()">VALUED_0:def 11</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"> (  not <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> or <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> is  <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:17_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> is  <a href="int_1.html#V1" title="INT_1:attr.1">integer</a> </span><br/>

<a NAME="E2:17_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_2.html#D1" target="_self" onmouseover="rs('euler_2/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:17_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="euler_2.html#D1" target="_self" onmouseover="rs('euler_2/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:17_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="euler_2.html#K2" title="EULER_2:func.2">mod</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> is  <a href="int_1.html#V1" title="INT_1:attr.1">integer</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"> verum</span><br/>


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