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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msafree2.html#V4" title="MSAFREE2:attr.4">finite-yielding</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">V</font> being    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">X</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b5">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b4">G</font>  st <font color="Olive" title="b3">X</font>,<font color="Olive" title="b1">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Olive" title="b5">C</font> holds <br/><font color="Olive" title="b5">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b3">X</font>,<font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msafree2.html#V4" title="MSAFREE2:attr.4">finite-yielding</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</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">  for <font color="Olive" title="b1">V</font> being    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font><br/>  for <font color="Olive" title="b2">X</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b4">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b3">G</font>  st <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Olive" title="b4">C</font> holds <br/><font color="Olive" title="b4">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">V</font> be    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">X</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font><br/>  for <font color="Olive" title="b2">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b3">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b2">G</font>  st <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Olive" title="b3">C</font> holds <br/><font color="Olive" title="b3">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font> be    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</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">  for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b1">G</font>  st <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Olive" title="b2">C</font> holds <br/><font color="Olive" title="b2">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c5">G</font>  st <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Olive" title="b1">C</font> holds <br/><font color="Olive" title="b1">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">C</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c5">G</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"> ( <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Maroon" title="c6">C</font> implies <font color="Maroon" title="c6">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> )</span><br/>











<span class="kw">given </span><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><a NAME="E2:79"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="circtrm1.html#D14" target="_self" onmouseover="rs('circtrm1/D14')" onmouseout="rh()">CIRCTRM1:def 14</a>,<a class="ref" href="circtrm1.html#D16" target="_self" onmouseover="rs('circtrm1/D16')" onmouseout="rh()">CIRCTRM1:def 16</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="c6">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="circtrm1.html#D15" target="_self" onmouseover="rs('circtrm1/D15')" onmouseout="rh()">CIRCTRM1:def 15</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">  ex <font color="Olive" title="b1">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ,<font color="Olive" title="b1">g</font> <a href="circtrm1.html#R4" title="CIRCTRM1:pred.4">form_embedding_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font> &amp; <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R3" title="CIRCTRM1:pred.3">preserves_inputs_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c8">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ,<font color="Maroon" title="c8">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R4" title="CIRCTRM1:pred.4">form_embedding_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font> &amp; <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R3" title="CIRCTRM1:pred.3">preserves_inputs_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:79"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ,<font color="Maroon" title="c8">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R4" title="CIRCTRM1:pred.4">form_embedding_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E53">A1</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"> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R3" title="CIRCTRM1:pred.3">preserves_inputs_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font></span><br/>

<a NAME="E4:79"/>
<font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ,<font color="Maroon" title="c8">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="circtrm1.html#T39" target="_self" onmouseover="rs('circtrm1/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:79"/>
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="circtrm1.html#R3" title="CIRCTRM1:pred.3">preserves_inputs_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T53" target="_self" onmouseover="rs('circtrm1/T53')" onmouseout="rh()">Th53</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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