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<b>reconsider </b><font color="Maroon" title="c2">A</font> =  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="finseq_1.html#T27" title="FINSEQ_1:th.27">FINSEQ_1:27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">A</font>;<br/><b>consider </b><font color="Maroon" title="c4">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:10_1_1_1"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">p</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> as   <a href="unialg_2.html#NM4" title="UNIALG_2:NM.4">PartFunc</a> of <font color="Maroon" title="c1">U0</font> <b>by </b><i><a class="txt" href="unialg_2.html#E2:10_1_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a></i>;<br/><a NAME="E4:10_1_1_1"/>
( <font color="Maroon" title="c5">p</font> is <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> &amp; <font color="Maroon" title="c5">p</font> is <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> &amp; not <font color="Maroon" title="c5">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:10_1_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="unialg_1.html#D5" title="UNIALG_1:def.5">UNIALG_1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:10_1_1_1"/>
<font color="Maroon" title="c3">x</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <a href="unialg_2.html#NM4" title="UNIALG_2:NM.4">PartFunc</a> of <font color="Maroon" title="c1">U0</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E2:10_1_1_1"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:10_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U0</font> is   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">PFuncsDomHQN</a> of <font color="Maroon" title="c1">U0</font>
 <b>by </b><i><a class="ref" href="unialg_2.html#D1" target="_self" title="UNIALG_2:def.1">Def1</a></i>;<br/>


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