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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Olive" title="b1">S</font>  st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font> holds <br/><span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b2">A</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" 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="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> holds <br/><span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b1">A</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> implies <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font> #) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">S1</font> =  <a href="facirc_2.html#K1" title="FACIRC_2:func.1">SingleMSS</a> <font color="Maroon" title="c1">x</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">A1</font> =  <a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font>;<br/>
<span class="kw">assume </span><a NAME="E1:10"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font> #)</span><br/>

<a NAME="E2:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<span class="p1">(<span class="default"><a href="facirc_2.html#K1" title="FACIRC_2:func.1">SingleMSS</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_2.html#T4" target="_self" title="FACIRC_2:th.4">Th5</a></span>;<br/>
<a NAME="E3:10"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<a NAME="E4:10"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" title="FACIRC_2:func.1">SingleMSS</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_2.html#D1" target="_self" title="FACIRC_2:def.1">Def1</a></span>;<br/>
<a NAME="E5:10"/><span class="lab"><font color="Green" title="E8">A5</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T57" title="CIRCCOMB:th.57">CIRCCOMB:57</a></span>;<br/>
<a NAME="E6:10"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" title="FACIRC_2:func.1">SingleMSS</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T57" title="CIRCCOMB:th.57">CIRCCOMB:57</a></span>;<br/>
<a NAME="E7:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A6</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <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="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<a NAME="E8:10"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E9:10"/><span class="kw">then </span>
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E10:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A7</font></span>: 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T20" title="FUNCT_4:th.20">FUNCT_4:20</a></span>;<br/>
<a NAME="E11:10"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="circcomb.html#D4" title="CIRCCOMB:def.4">CIRCCOMB:def 4</a></span>;<br/>
<a NAME="E12:10"/><span class="lab"><font color="Green" title="E12">A9</font></span>: 
 the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="circcomb.html#D4" title="CIRCCOMB:def.4">CIRCCOMB:def 4</a></span>;<br/>
<a NAME="E13:10"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
 <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 <span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" title="FACIRC_2:func.1">SingleMSS</a> <font color="Maroon" title="c1">x</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E14:10"/>
 <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="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:10"/>
<span class="p1">(<span class="default"><a href="facirc_2.html#K2" title="FACIRC_2:func.2">SingleMSA</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c3">A</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="ref" href="funct_4.html#T19" title="FUNCT_4:th.19">FUNCT_4:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
