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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1_1_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_1_1"><b>suppose </b></a><a NAME="E1:16_1_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><a NAME="E2:16_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font> is   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="pre_topc.html#T30">PRE_TOPC:30</a></i>;<br/><a NAME="E3:16_1_1_1_1"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>hence </b><a NAME="E4:16_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_1_2"><b>suppose </b></a><a NAME="E1:16_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a>  ;<br/><a NAME="E3:16_1_1_1_2"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E4:16_1_1_1_2"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><b>hence </b><a NAME="E5:16_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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