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<span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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></span><br/><span class="kw">consider </span><font color="Maroon" title="c4">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E2:10_1_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:10_1_1_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="unialg_1.html#T5" title="UNIALG_1:th.5">UNIALG_1:5</a></span>;<br/><a NAME="E5:10_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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></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></span>;<br/><span class="kw">hence </span><a NAME="E6:10_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D1" target="_self" title="UNIALG_2:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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