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<span class="kw">let </span><font color="Maroon" title="c1">IIG</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="msafree2.html#V5" title="MSAFREE2:attr.5">monotonic</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">SCS</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="c1">IIG</font><br/>  for <font color="Olive" title="b2">v</font> being   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">IIG</font><br/>  for <font color="Olive" title="b3">iv</font> being    <a href="msafree2.html#M1" title="MSAFREE2:mode.1">InputValues</a> of <font color="Olive" title="b1">SCS</font>  st <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> holds <br/> <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Olive" title="b1">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">v</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">p</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">SCS</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="c1">IIG</font>; <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">v</font> being   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">IIG</font><br/>  for <font color="Olive" title="b2">iv</font> being    <a href="msafree2.html#M1" title="MSAFREE2:mode.1">InputValues</a> of <font color="Maroon" title="c3">SCS</font>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> holds <br/> <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">IIG</font>; <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">iv</font> being    <a href="msafree2.html#M1" title="MSAFREE2:mode.1">InputValues</a> of <font color="Maroon" title="c3">SCS</font>  st <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> holds <br/> <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Maroon" title="c4">v</font>,<font color="Olive" title="b1">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">iv</font> be    <a href="msafree2.html#M1" title="MSAFREE2:mode.1">InputValues</a> of <font color="Maroon" title="c3">SCS</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="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> implies  <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>





<span class="kw">assume </span><a NAME="E2:16"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">e</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>;<br/>
<a NAME="E3:16"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font>
 
;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">X</font> =  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">F</font> =  <a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font>;<br/>
<a NAME="E4:16"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">IIG</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E5:16"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">IIG</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">o</font> =  <a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font>;<br/>
<a NAME="E6:16"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
 <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">IIG</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#T3" title="MSAFREE2:th.3">MSAFREE2:3</a></span>;<br/>
<a NAME="E7:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="msafree2.html#D7" title="MSAFREE2:def.7">MSAFREE2:def 7</a></span>;<br/>
<a NAME="E8:16"/>
 <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">IIG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">v1</font> where <font color="Olive" title="b1">v1</font> is   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">IIG</font> : <font color="Olive" title="b1">v1</font> is  <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a>  </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#D1" title="MSAFREE2:def.1">MSAFREE2:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">x9</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">IIG</font><span class="kw"> such that </span><br/><a NAME="E10:16"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c10">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">and </span><br/><a NAME="E11:16"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c10">x9</font> is  <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">o1</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">IIG</font><span class="kw"> such that </span><br/><a NAME="E13:16"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">o1</font> <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">and </span><br/><a NAME="E14:16"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
 the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="msualg_2.html#D1" title="MSUALG_2:def.1">MSUALG_2:def 1</a></span>;<br/>
<a NAME="E15:16"/>
 the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c11">o1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D2" title="MSUALG_1:def.2">MSUALG_1:def 2</a></span>;<br/>
<a NAME="E16:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A11</font></span>: 
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="msafree2.html#D7" title="MSAFREE2:def.7">MSAFREE2:def 7</a></span>;<br/>
<span class="lab"><font color="Green" title="E27">A12</font></span>:  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p2">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="pre_circ.html#T2" title="PRE_CIRC:th.2">PRE_CIRC:2</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">x</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>) <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">Fx</font> = <span class="p1">(<span class="default"><a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c12">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>) ;<br/>
<a NAME="E20:16"/>
 <a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font>,<font color="Maroon" title="c3">SCS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#D9" title="MSAFREE2:def.9">MSAFREE2:def 9</a></span>;<br/>
<a NAME="E21:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p3">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">Fx</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#D7" title="MSUALG_3:def.7">MSUALG_3:def 7</a></span>;<br/>
<a NAME="E22:16"/><span class="lab"><font color="Green" title="E29">A14</font></span>: 
 <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K8" title="MSAFREE:func.8">FreeSort</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K10" title="MSAFREE:func.10">FreeOper</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree.html#D14" title="MSAFREE:def.14">MSAFREE:def 14</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E30">A15</font></span>:  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>) = 
<span class="p1">(<span class="default"><a href="msafree.html#K10" title="MSAFREE:func.10">FreeOper</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D6" title="MSUALG_1:def.6">MSUALG_1:def 6</a></span>
<br/>.= 
 <a href="msafree.html#K9" title="MSAFREE:func.9">DenOp</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree.html#D13" title="MSAFREE:def.13">MSAFREE:def 13</a></span>
;<br/>
<a NAME="E24:16"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:16"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E25:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A16</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K8" title="MSAFREE:func.8">FreeSort</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:16"><span class="lab"><font color="Green" title="E29">A14</font></span></a>, <a class="ref" href="msualg_1.html#D4" title="MSUALG_1:def.4">MSUALG_1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">p9</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree.html#T8" title="MSAFREE:th.8">MSAFREE:8</a></span>;<br/>
<a NAME="E27:16"/>
 <a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font>) <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c14">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:16"><span class="lab"><font color="Green" title="E31">A16</font></span></a>, <a class="ref" href="msafree.html#T10" title="MSAFREE:th.10">MSAFREE:10</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E32">A17</font></span>: <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> = 
<span class="p1">(<span class="default"><a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> (<span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font>)</span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:16"><span class="lab"><font color="Green" title="E30">A15</font></span></a>, <a class="ref" href="msafree.html#D12" title="MSAFREE:def.12">MSAFREE:def 12</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</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="msafree.html#D9" title="MSAFREE:def.9">MSAFREE:def 9</a></span>
<br/>.= 
 <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#T20" title="TREES_4:th.20">TREES_4:20</a></span>
;<br/>
<a NAME="E29:16"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E30:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A18</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E32">A17</font></span></a>, <a class="txt" href="#E21:16"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
 <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>,<font color="Maroon" title="c3">SCS</font>) = 
<span class="p1">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D5" title="MSUALG_1:def.5">MSUALG_1:def 5</a></span>
<br/>.= 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">e</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K6" title="MSAFREE2:func.6">Eval</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">action_at</a> <font color="Maroon" title="c4">v</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">IIG</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E32">A17</font></span></a>, <a class="txt" href="#E21:16"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="msualg_1.html#D2" title="MSUALG_1:def.2">MSUALG_1:def 2</a></span>;<br/>
<a NAME="E33:16"/>
 ex <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">A</font> <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 <font color="Maroon" title="c3">SCS</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> &amp;  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c3">SCS</font>,<font color="Maroon" title="c4">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">a</font> where <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font> :  ex <font color="Olive" title="b3">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">IIG</font> st <br/>(  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">IIG</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Olive" title="b3">o</font>,<font color="Maroon" title="c3">SCS</font>)</span>)</span> ) </span> } </span>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D3" title="MSUALG_2:def.3">MSUALG_2:def 3</a></span>;<br/>
<a NAME="E34:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A19</font></span>: 
<font color="Maroon" title="c15">e</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="c3">SCS</font>,<font color="Maroon" title="c4">v</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E30:16"><span class="lab"><font color="Green" title="E33">A18</font></span></a></span>;<br/>
<a NAME="E35:16"/>
 ex <font color="Olive" title="b1">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">FreeEnv</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> st <br/>(  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit1.html#K4" title="CIRCUIT1:func.4">size</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">SCS</font>) &amp;  <a href="circuit2.html#K4" title="CIRCUIT2:func.4">IGTree</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">iv</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" title="CIRCUIT2:func.3">Fix_inp_ext</a> <font color="Maroon" title="c5">iv</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">e</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circuit2.html#D3" target="_self" title="CIRCUIT2:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span> <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">iv</font>) = 
<font color="Maroon" title="c15">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="circuit2.html#T5" target="_self" title="CIRCUIT2:th.5">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit1.html#K1" title="CIRCUIT1:func.1">Set-Constants</a> <font color="Maroon" title="c3">SCS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E34:16"><span class="lab"><font color="Green" title="E34">A19</font></span></a>, <a class="ref" href="circuit1.html#T1" title="CIRCUIT1:th.1">CIRCUIT1:1</a></span>
;<br/> <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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