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<span class="kw">set </span><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">C</font> = <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">D</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> )</span><br/><span class="kw">assume </span><a NAME="E1:157_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span>
 ; <a class="txt" 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">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">xx</font> = <font color="Maroon" title="c5">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> ;<br/><a NAME="E3:157_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">xx</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 ;<br/><span class="kw">hence </span><a NAME="E4:157_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:157_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">U</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a>  holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="pre_poly.html#V1" title="PRE_POLY:attr.1">FinSequence-yielding</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D3" title="PRE_POLY:def.3">PRE_POLY:def 3</a></span>; <a class="txt" 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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