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<span class="kw">set </span><font color="Maroon" title="c3">S1</font> = <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">S2</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">a1</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">a2</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">o1</font> =  the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:131_1_1"/><span class="lab"><font color="Green" title="E38">B0</font></span>: 
(  <a href="fomodel1.html#K7" title="FOMODEL1:func.7">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K7" title="FOMODEL1:func.7">TheEqSymbOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font></span>)</span> &amp;  <a href="fomodel1.html#K8" title="FOMODEL1:func.8">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K8" title="FOMODEL1:func.8">TheNorSymbOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D42" target="_self" title="FOMODEL1:def.42">DefExt1</a></span>;<br/>
<a NAME="E2:131_1_1"/>
 the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D42" target="_self" title="FOMODEL1:def.42">DefExt1</a></span>;<br/>
<a NAME="E3:131_1_1"/><span class="kw">then </span>
 the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c1">S</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:131_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K40" title="FOMODEL1:func.40">extendWith</a> <font color="Maroon" title="c2">f</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:131_1_1"><span class="lab"><font color="Green" title="E38">B0</font></span></a>, <a class="ref" href="fomodel1.html#D41" target="_self" title="FOMODEL1:def.41">DefExt0</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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