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<b>consider </b><font color="Maroon" title="c4">A1</font> being   <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S1</font><b> such that </b><br/><a NAME="E2:66_1_1"/><i><font color="Green" title="E32">A1</font></i>: 
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c4">A1</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> )
 <b>by </b><i><a class="ref" href="circcmb3.html#D9" target="_self" title="CIRCCMB3:def.9">Def9</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">A2</font> being   <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S2</font><b> such that </b><br/><a NAME="E4:66_1_1"/><i><font color="Green" title="E33">A2</font></i>: 
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">A2</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> )
 <b>by </b><i><a class="ref" href="circcmb3.html#D9" target="_self" title="CIRCCMB3:def.9">Def9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">A1</font> = <font color="Maroon" title="c4">A1</font> as    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">S1</font> <b>by </b><i><a class="txt" href="#E2:66_1_1"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">A2</font> = <font color="Maroon" title="c5">A2</font> as    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S2</font> <b>by </b><i><a class="txt" href="#E4:66_1_1"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">A</font> = <font color="Maroon" title="c6">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c7">A2</font> as   <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c3">S2</font> <b>by </b><i><a class="ref" href="circcmb3.html#T31" target="_self" title="CIRCCMB3:th.31">Th31</a></i>;<br/>
<a NAME="E8:66_1_1"/>
<font color="Maroon" title="c2">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c3">S2</font> is    <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c1">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon" title="c8">A</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="circcmb3.html#D9" target="_self" title="CIRCCMB3:def.9">CIRCCMB3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c8">A</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c8">A</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> )</span><br/>

<b>thus </b><a NAME="E1:66_1_1_1"/>
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c8">A</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp;  <a href="yellow_6.html#K1" title="YELLOW_6:func.1">the_value_of</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="circcmb3.html#T33" target="_self" title="CIRCCMB3:th.33">Th33</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="c8">A</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a></span><br/>

<b>thus </b><a NAME="E2:66_1_1_1"/>
<font color="Maroon" title="c8">A</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a>
 <b>by </b><i><a class="ref" href="circcmb3.html#T32" target="_self" title="CIRCCMB3:th.32">Th32</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="E9:66_1_1"/>
<font color="Maroon" title="c2">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c3">S2</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c1">X</font>
 ; <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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