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<b>set </b><font color="Maroon" title="c3">e</font> =  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">F</font>;<br/>
<b>let </b><font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c5">u2</font> be   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</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">u1</font> <a href="finseqop.html#R1" title="FINSEQOP:pred.1">is_an_inverseOp_wrt</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c5">u2</font> <a href="finseqop.html#R1" title="FINSEQOP:pred.1">is_an_inverseOp_wrt</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:71_1_1"/><i><font color="Green" title="E33">A4</font></i>: 
for <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds <br/> ( <font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">d</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">d</font></span>)</span>,<font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">F</font> )
 <b>and </b><br/><a NAME="E2:71_1_1"/><i><font color="Green" title="E34">A5</font></i>: 
for <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds <br/> ( <font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">d</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">d</font></span>)</span>,<font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">F</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="finseqop.html#D1" target="_self" title="FINSEQOP:def.1">FINSEQOP:def 1</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">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span><br/><b>set </b><font color="Maroon" title="c7">d1</font> = <font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font>;<br/><b>set </b><font color="Maroon" title="c8">d2</font> = <font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font>;<br/><b>thus </b><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font> = 
<font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</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="c2">F</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="setwiseo.html#T23" title="SETWISEO:th.23">SETWISEO:23</a></i>
<br/>.= 
<font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c6">d</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:71_1_1"><i><font color="Green" title="E34">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span>)</span>,<font color="Maroon" title="c6">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="binop_1.html#D3" title="BINOP_1:def.3">BINOP_1:def 3</a></i>
<br/>.= 
<font color="Maroon" title="c2">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="c2">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:71_1_1"><i><font color="Green" title="E33">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">u2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">d</font>
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E30">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="E4:71_1_1"/>
<font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</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/>


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