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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:4_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K3">rngs</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><a NAME="E2:4_1_1_1"/><b>then </b><i><font color="Green">E1</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_6.html#T90">FUNCT_6:90</a></i>;<br/><a NAME="E3:4_1_1_1"/><b>then </b><i><font color="Green">E2</font></i>: 
<span class="p1">(<span class="default"><a href="funct_6.html#K3">rngs</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_6.html#T31">FUNCT_6:31</a></i>;<br/><a NAME="E4:4_1_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="jordan1h.html#E2:4_1_1_1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/><b>hence </b><a NAME="E5:4_1_1_1"/>
not <span class="p1">(<span class="default"><a href="funct_6.html#K3">rngs</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="jordan1h.html#E3:4_1_1_1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:4_1_1"/>
 <a href="funct_6.html#K3">rngs</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_1.html#V2">non-empty</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/>


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