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<span class="kw">set </span><font color="Maroon" title="c5">sc</font> =  <a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font>;<br/>
<a NAME="E1:21_1_1"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</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/>
<div><span class="lab"><font color="Green" title="E20">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> implies <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:21_1_1_1"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span>
 ; <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="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">v</font> = <font color="Maroon" title="c6">x</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">IIG</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a></span>;<br/><a NAME="E3:21_1_1_1"/>
<span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">SCS</font>,<font color="Maroon" title="c7">v</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1_1_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="circuit1.html#D1" title="CIRCUIT1:def.1">CIRCUIT1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:21_1_1_1"/>
<span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 ; <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><span class="kw">end;</span></div>
<a NAME="E3:21_1_1"/>
 <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="c2">SCS</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="c1">IIG</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="E4:21_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="circuit2.html#K1" title="CIRCUIT2:func.1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="circuit1.html#K2" title="CIRCUIT1:func.2">-th_InputValues</a> <font color="Maroon" title="c3">InpFs</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c2">SCS</font></span>)</span> is   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">SCS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:21_1_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="pre_circ.html#T6" title="PRE_CIRC:th.6">PRE_CIRC:6</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/>


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