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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">E</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c2">Y</font><br/>  for <font color="Olive" title="b3">g</font> being  <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c2">Y</font><br/>  for <font color="Olive" title="b2">g</font> being  <font color="Maroon" title="c3">E</font>,<font color="Olive">b<sub>1</sub></font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Olive" title="b1">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being  <font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">g</font> be  <font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>; <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="c4">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">G</font> = <font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>);<br/>
<a NAME="E1:86"/><span class="lab"><font color="Green" title="E31">B1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">LH</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c8">RH</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c4">F</font></span>)</span> ;<br/>
<a NAME="E3:86"/><span class="lab"><font color="Green" title="E32">B0</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">LH</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">RH</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <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="c7">LH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">RH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c10">F1</font> = <font color="Maroon" title="c7">LH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font>, <font color="Maroon" title="c11">F2</font> = <font color="Maroon" title="c8">RH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c4">F</font> ;<br/><a NAME="E2:86_1"/><span class="lab"><font color="Green" title="E33">C3</font></span>: 
( <font color="Maroon" title="c10">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span> &amp; <font color="Maroon" title="c11">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E32">B0</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/><a NAME="E3:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c9">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel3.html#D13" target="_self" title="FOMODEL3:def.13">DefClass</a></span>;<br/><a NAME="E4:86_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c9">x</font>)</span>)</span>,<font color="Maroon" title="c11">F2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:86"><span class="lab"><font color="Green" title="E31">B1</font></span></a>, <a class="ref" href="funct_1.html#T1" title="FUNCT_1:th.1">FUNCT_1:1</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">e</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c3">E</font>, <font color="Maroon" title="c13">f</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c4">F</font><span class="kw"> such that </span><br/><a NAME="E6:86_1"/><span class="lab"><font color="Green" title="E34">C0</font></span>: 
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c9">x</font>)</span>)</span>,<font color="Maroon" title="c11">F2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">e</font>,<font color="Maroon" title="c13">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">e</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">f</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">g</font> ) )
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:86_1"/><span class="lab"><font color="Green" title="E35">C1</font></span>: 
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">e</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">f</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c15">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">g</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:86_1"><span class="lab"><font color="Green" title="E34">C0</font></span></a></span>;<br/><a NAME="E9:86_1"/><span class="lab"><font color="Green" title="E36">Z2</font></span>: 
(  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c9">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">e</font> &amp; <font color="Maroon" title="c11">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">f</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:86_1"><span class="lab"><font color="Green" title="E34">C0</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E10:86_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">C2</font></span>: 
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c9">x</font>) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c9">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">E</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:86_1"><span class="lab"><font color="Green" title="E35">C1</font></span></a>, <a class="ref" href="eqrel_1.html#T19" title="EQREL_1:th.19">EQREL_1:19</a></span>;<br/><a NAME="E11:86_1"/>
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:86_1"><span class="lab"><font color="Green" title="E35">C1</font></span></a></span>;<br/><a NAME="E12:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a</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> <font color="Maroon" title="c5">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E13:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:86_1"><span class="lab"><font color="Green" title="E35">C1</font></span></a>, <a class="ref" href="funct_1.html#D2" title="FUNCT_1:def.2">FUNCT_1:def 2</a></span>;<br/><a NAME="E14:86_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:86_1"><span class="lab"><font color="Green" title="E37">C2</font></span></a>, <a class="ref" href="fomodel3.html#D9" target="_self" title="FOMODEL3:def.9">DefCompatible</a></span>;<br/><a NAME="E15:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">EqClass</a> (<font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T19" title="EQREL_1:th.19">EQREL_1:19</a></span>;<br/><a NAME="E16:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">F1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:86_1"><span class="lab"><font color="Green" title="E33">C3</font></span></a>, <a class="ref" href="fomodel3.html#D13" target="_self" title="FOMODEL3:def.13">DefClass</a></span>;<br/><a NAME="E17:86_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">F1</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> <font color="Maroon" title="c11">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:86_1"><span class="lab"><font color="Green" title="E35">C1</font></span></a>, <a class="txt" href="#E9:86_1"><span class="lab"><font color="Green" title="E36">Z2</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><span class="kw">hence </span><a NAME="E18:86_1"/>
<font color="Maroon" title="c7">LH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">RH</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D4" title="EQREL_1:def.4">EQREL_1:def 4</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:86"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="fomodel3.html#K16" title="FOMODEL3:func.16">quotient</a> (<font color="Maroon" title="c3">E</font>,<font color="Maroon" title="c4">F</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="fomodel3.html#K17" title="FOMODEL3:func.17">-class</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</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/>


</div>
