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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>  st (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font>) ) &amp; (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font>) ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">M</font> =  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> =  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> ($1,<font color="Maroon" title="c1">S</font>);<br/>
<a NAME="E1:130"/>
 for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>  st (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">f</font>) ) &amp; (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">f</font>) ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</font>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="modelc_1.html#S5" onmouseover="rs('modelc_1/S5')" onmouseout="rh()">MODELC_1:sch 5</a>();<br/></span>
<span class="kw">hence </span><a NAME="E2:130"/>
 for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>  st (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font>) ) &amp; (  for <font color="Olive" title="b3">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b2">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K33" title="MODELC_2:func.33">Next_0</a> (<font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">S</font>) ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</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"> verum</span><br/>


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