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<b>let </b><font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c2">C</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">F</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b2">F</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  holds <br/>( <font color="Olive" title="b2">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span>,<font color="Olive" title="b1">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b2">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> )</span><br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b1">F</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  holds <br/>( <font color="Olive" title="b1">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Olive" title="b1">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> )</span><br/><b>let </b><font color="Maroon" title="c4">F</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  implies ( <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> ) )</span><br/>







<b>assume </b><a NAME="E1:53"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font> )</span><br/>

<b>set </b><font color="Maroon" title="c5">e</font> =  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">g</font> = <font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">D</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font> = 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T48" title="FUNCOP_1:th.48">FUNCOP_1:48</a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font>
<b>by </b><i><a class="txt" href="finseqop.html#E1:53"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="setwiseo.html#T23" title="SETWISEO:th.23">SETWISEO:23</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:53"/>
<font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font> = 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T48" title="FUNCOP_1:th.48">FUNCOP_1:48</a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font>
<b>by </b><i><a class="txt" href="finseqop.html#E1:53"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="setwiseo.html#T23" title="SETWISEO:th.23">SETWISEO:23</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:53"/>
<font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c3">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
