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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span> ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Olive" title="b1">x</font>) &amp; $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Olive" title="b2">y</font>) &amp; $3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)) );<br/>
<a NAME="E1:97_1"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() holds <br/> ex <font color="Olive" title="b3">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>] )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="97_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() implies  ex <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>] ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:97_1_1"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()
 <span class="kw">and </span><br/><a NAME="E2:97_1_1"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font>] )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">a1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:97_1_1"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 <span class="kw">and </span><br/><a NAME="E5:97_1_1"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">a1</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="eqrel_1.html#D3" onmouseover="rs('eqrel_1/D3')" onmouseout="rh()">EQREL_1:def 3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">b1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E7:97_1_1"/><span class="lab"><font color="Green" title="E43">A7</font></span>: 
<font color="Maroon" title="c4">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 <span class="kw">and </span><br/><a NAME="E8:97_1_1"/><span class="lab"><font color="Green" title="E44">A8</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c4">b1</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="eqrel_1.html#D3" onmouseover="rs('eqrel_1/D3')" onmouseout="rh()">EQREL_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">a1</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c6">b1</font> = <font color="Maroon" title="c4">b1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97_1_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E7:97_1_1"><span class="lab"><font color="Green" title="E43">A7</font></span></a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c7">c</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">b1</font>)); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c7">c</font>] )</span><br/>

<span class="kw">thus </span><a NAME="E10:97_1_1"/>
<font color="Maroon" title="c7">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" onmouseover="rs('eqrel_1/D3')" onmouseout="rh()">EQREL_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c7">c</font>]</span><br/>

<span class="kw">thus </span><a NAME="E11:97_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c7">c</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97_1_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="txt" href="#E8:97_1_1"><span class="lab"><font color="Green" title="E44">A8</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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">consider </span><font color="Maroon" title="c1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>,<span class="p2">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span><span class="kw"> such that </span><br/><a NAME="E3:97_1"/><span class="lab"><font color="Green" title="E39">A10</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S1" onmouseover="rs('binop_1/S1')" onmouseout="rh()">BINOP_1:sch 1</a>(<a class="txt" href="#E1:97_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a>);<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c1">f</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds  <font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Olive" title="b1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Olive" title="b2">y</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>))</span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>))</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">u</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c5">v</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>);<br/>
<a NAME="E4:97_1"/>
(  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>() )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" onmouseover="rs('eqrel_1/D3')" onmouseout="rh()">EQREL_1:def 3</a></span>;<br/>
<a NAME="E5:97_1"/><span class="kw">then </span>
<font color="Maroon">S<sub>1</sub></font>[ <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>), <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>),<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>)</span>)</span>)]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1"><span class="lab"><font color="Green" title="E39">A10</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">x1</font>, <font color="Maroon" title="c7">y1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<span class="kw"> such that </span><br/><a NAME="E7:97_1"/><span class="lab"><font color="Green" title="E40">A11</font></span>: 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c6">x1</font>)
 <span class="kw">and </span><br/><a NAME="E8:97_1"/><span class="lab"><font color="Green" title="E41">A12</font></span>: 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c7">y1</font>)
 <span class="kw">and </span><br/><a NAME="E9:97_1"/><span class="lab"><font color="Green" title="E42">A13</font></span>: 
<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c6">x1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c7">y1</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c7">y1</font>))
 ;<br/>
<a NAME="E10:97_1"/>
( <font color="Maroon" title="c6">x1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>) &amp; <font color="Maroon" title="c7">y1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="txt" href="#E8:97_1"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="ref" href="eqrel_1.html#T23" onmouseover="rs('eqrel_1/T23')" onmouseout="rh()">EQREL_1:23</a></span>;<br/>
<a NAME="E11:97_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="c2">x</font>,<font color="Maroon" title="c6">x1</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">F<sub>3</sub></font>() &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c7">y1</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">F<sub>3</sub></font>() )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T18" onmouseover="rs('eqrel_1/T18')" onmouseout="rh()">EQREL_1:18</a></span>;<br/>
<a NAME="E12:97_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">F<sub>2</sub></font>(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c7">y1</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">F<sub>3</sub></font>()
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>;<br/>
<a NAME="E13:97_1"/><span class="kw">then </span>
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c6">x1</font>,<font color="Maroon" title="c7">y1</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>))
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T18" onmouseover="rs('eqrel_1/T18')" onmouseout="rh()">EQREL_1:18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:97_1"/>
<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c2">x</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c3">y</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>))
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="txt" href="#E8:97_1"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="txt" href="#E9:97_1"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="ref" href="eqrel_1.html#T23" onmouseover="rs('eqrel_1/T23')" onmouseout="rh()">EQREL_1:23</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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