<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S1</font>, <font color="Olive" title="b2">S2</font> being   <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">A1</font> being   <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">S1</font><br/> for <font color="Olive" title="b4">A2</font> being   <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">S2</font> holds  <font color="Olive" title="b3">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b4">A2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S1</font>, <font color="Maroon" title="c3">S2</font> be    <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being   <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><br/> for <font color="Olive" title="b2">A2</font> being   <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> holds  <font color="Olive" title="b1">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A1</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A2</font> being   <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> holds  <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">A2</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">A2</font></span><br/>







<span class="kw">thus </span><a NAME="E1:61"/>
<font color="Maroon" title="c2">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c3">S2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T55" title="CIRCCOMB:th.55">CIRCCOMB:55</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="circcomb.html#D3" title="CIRCCOMB:def.3">CIRCCOMB:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">A2</font> )</span><br/>

<a NAME="E2:61"/>
( 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="funct_1.html#K3" title="FUNCT_1:func.3">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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></span>;<br/>
<a NAME="E3:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A1</font></span>: 
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> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T95" title="FUNCOP_1:th.95">FUNCOP_1:95</a></span>;<br/>
<a NAME="E4:61"/>
( 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="funct_1.html#K3" title="FUNCT_1:func.3">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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></span>;<br/>
<a NAME="E5:61"/><span class="kw">then </span>
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> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A1</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T95" title="FUNCOP_1:th.95">FUNCOP_1:95</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:61"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">A2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="circcomb.html#T4" title="CIRCCOMB:th.4">CIRCCOMB:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">A2</font></span><br/>

<span class="kw">thus </span><a NAME="E7:61"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">A2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T56" title="CIRCCOMB:th.56">CIRCCOMB:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
