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<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <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">  for <font color="Olive" title="b1">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">A</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b3">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Olive" title="b3">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</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="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">x</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">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</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="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:38"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c1">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</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="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font></span><br/>

<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">A</font> = 
 <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="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E19">A2</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T12" target="_self" onmouseover="rs('funcop_1/T12')" onmouseout="rh()">Th12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T12" target="_self" onmouseover="rs('funcop_1/T12')" onmouseout="rh()">Th12</a></span>
;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> (<font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> (<font color="Maroon" title="c2">g</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="funcop_1.html#T23" target="_self" onmouseover="rs('funcop_1/T23')" onmouseout="rh()">Th23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> (<font color="Maroon" title="c2">g</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:38"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="funcop_1.html#T24" target="_self" onmouseover="rs('funcop_1/T24')" onmouseout="rh()">Th24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K4" title="FUNCOP_1:func.4">[:]</a> (<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c3">A</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"> verum</span><br/>


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