<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">  for <font color="Olive" title="b1">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds   <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">gf</font> = <font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font>;<br/>
<a NAME="E1:72"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D6" onmouseover="rs('fomodel2/D6')" onmouseout="rh()">FOMODEL2:def 6</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:72"/>
 <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="72_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:72_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</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" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:72_1"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#T1" target="_self" onmouseover="rs('flexary1/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<a NAME="E4:72_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="fomodel2.html#D6" onmouseover="rs('fomodel2/D6')" onmouseout="rh()">FOMODEL2:def 6</a>, <a class="txt" href="#E3:72_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a></span>;<br/>
<a NAME="E5:72_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A3</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font></span>)</span> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="funct_1.html#T11" onmouseover="rs('funct_1/T11')" onmouseout="rh()">FUNCT_1:11</a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>;<br/>
<a NAME="E6:72_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E3:72_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="flexary1.html#T1" target="_self" onmouseover="rs('flexary1/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:72_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:72_1"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="txt" href="#E3:72_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="funct_1.html#D6" onmouseover="rs('funct_1/D6')" onmouseout="rh()">FUNCT_1:def 6</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">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</span> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:72"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font></span>)</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" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E5:72"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c2">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D6" onmouseover="rs('funct_1/D6')" onmouseout="rh()">FUNCT_1:def 6</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E7:72"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:72"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="flexary1.html#T1" target="_self" onmouseover="rs('flexary1/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<a NAME="E8:72"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
( <font color="Maroon" title="c2">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:72"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E7:72"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="funct_1.html#T11" onmouseover="rs('funct_1/T11')" onmouseout="rh()">FUNCT_1:11</a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<a NAME="E9:72"/>
( <font color="Maroon" title="c2">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:72"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="fomodel2.html#D6" onmouseover="rs('fomodel2/D6')" onmouseout="rh()">FOMODEL2:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:72"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#T1" target="_self" onmouseover="rs('flexary1/T1')" onmouseout="rh()">Th1</a>, <a class="txt" href="#E5:72"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E7:72"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E8:72"><span class="lab"><font color="Green" title="E42">A6</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/>


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