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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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">X</font> being   <a href="zf_refle.html#NM1" title="ZF_REFLE:NM.1">Subclass</a> of <font color="Maroon" title="c1">V</font><br/>  for <font color="Olive" title="b2">E</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 <font color="Olive" title="b1">X</font> is  <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a>  &amp; <font color="Olive" title="b2">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/> for <font color="Olive" title="b3">H</font>, <font color="Olive" title="b4">H9</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b3">H</font>,<font color="Olive" title="b2">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp;  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b4">H9</font>,<font color="Olive" title="b2">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/> <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b4">H9</font></span>)</span>,<font color="Olive" title="b2">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   <a href="zf_refle.html#NM1" title="ZF_REFLE:NM.1">Subclass</a> of <font color="Maroon" title="c1">V</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">E</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 <font color="Maroon" title="c2">X</font> is  <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a>  &amp; <font color="Olive" title="b1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> holds <br/> for <font color="Olive" title="b2">H</font>, <font color="Olive" title="b3">H9</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b2">H</font>,<font color="Olive" title="b1">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b3">H9</font>,<font color="Olive" title="b1">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> holds <br/> <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b3">H9</font></span>)</span>,<font color="Olive" title="b1">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be   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> ; <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="c2">X</font> is  <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a>  &amp; <font color="Maroon" title="c3">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies  for <font color="Olive" title="b1">H</font>, <font color="Olive" title="b2">H9</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b2">H9</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> holds <br/> <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c2">X</font> is  <a href="zf_fund1.html#V8" title="ZF_FUND1:attr.8">closed_wrt_A1-A7</a> 
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c3">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</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">H</font>, <font color="Olive" title="b2">H9</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b1">H</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Olive" title="b2">H9</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> holds <br/> <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">E9</font> = <font color="Maroon" title="c3">E</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E49">A2</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">H</font>, <font color="Maroon" title="c6">H9</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:45"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
 <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E5:45"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
 <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">fs</font> =  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">fs9</font> =  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">D1</font> =  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>), <font color="Maroon" title="c10">D2</font> =  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>) as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E51">A4</font></span></a></span>;<br/>
<a NAME="E7:45"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">E9</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="zf_fund1.html#T9" target="_self" title="ZF_FUND1:th.9">Th9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">F1</font> =  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">E9</font>) as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E9:45"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">E9</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="zf_fund1.html#T9" target="_self" title="ZF_FUND1:th.9">Th9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">F2</font> =  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">E9</font>) as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">A</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">B</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> ;<br/>
<a NAME="E11:45"/><span class="lab"><font color="Green" title="E54">A7</font></span>: 
<font color="Maroon" title="c2">X</font> is  <a href="zf_fund1.html#V5" title="ZF_FUND1:attr.5">closed_wrt_A5</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="zf_fund1.html#D13" target="_self" title="ZF_FUND1:def.13">Def13</a></span>;<br/>
<a NAME="E12:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A8</font></span>: 
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E9:45"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="zf_fund1.html#D10" target="_self" title="ZF_FUND1:def.10">Def10</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">p</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="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span>  implies <font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) )</span><br/><span class="kw">assume </span><a NAME="E1:45_1"/><span class="lab"><font color="Green" title="E56">A9</font></span>: 
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> 
 ; <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="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)</span><br/><a NAME="E2:45_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">x</font>, <font color="Maroon" title="c17">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E4:45_1"/><span class="lab"><font color="Green" title="E57">A10</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Maroon" title="c17">y</font>
 <span class="kw">and </span><br/><a NAME="E5:45_1"/><span class="lab"><font color="Green" title="E58">A11</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font>
 <span class="kw">and </span><br/><a NAME="E6:45_1"/><span class="lab"><font color="Green" title="E59">A12</font></span>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font>
 ;<br/><a NAME="E7:45_1"/>
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c18">x9</font>, <font color="Maroon" title="c19">y9</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E9:45_1"/><span class="lab"><font color="Green" title="E60">A13</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x9</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Maroon" title="c19">y9</font>
 <span class="kw">and </span><br/><a NAME="E10:45_1"/><span class="lab"><font color="Green" title="E61">A14</font></span>: 
<font color="Maroon" title="c18">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font>
 <span class="kw">and </span><br/><a NAME="E11:45_1"/><span class="lab"><font color="Green" title="E62">A15</font></span>: 
<font color="Maroon" title="c19">y9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font>
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c20">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c3">E</font><span class="kw"> such that </span><br/><a NAME="E13:45_1"/><span class="lab"><font color="Green" title="E63">A16</font></span>: 
<font color="Maroon" title="c18">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E14:45_1"/><span class="lab"><font color="Green" title="E64">A17</font></span>: 
<font color="Maroon" title="c20">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:45_1"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c21">e</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E16:45_1"/><span class="lab"><font color="Green" title="E65">A18</font></span>: 
<font color="Maroon" title="c17">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">e</font>
 <span class="kw">and </span><br/><a NAME="E17:45_1"/><span class="lab"><font color="Green" title="E66">A19</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c21">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E18:45_1"/><span class="lab"><font color="Green" title="E67">A20</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c21">e</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:45_1"><span class="lab"><font color="Green" title="E59">A12</font></span></a>, <a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c22">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c3">E</font><span class="kw"> such that </span><br/><a NAME="E20:45_1"/><span class="lab"><font color="Green" title="E68">A21</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E21:45_1"/><span class="lab"><font color="Green" title="E69">A22</font></span>: 
<font color="Maroon" title="c22">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45_1"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</a></span>;<br/><a NAME="E22:45_1"/><span class="lab"><font color="Green" title="E70">A23</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="zf_fund1.html#E16"><span class="lab"><font color="Green" title="E15">Lm3</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">gg</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c21">e</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:45_1"><span class="lab"><font color="Green" title="E66">A19</font></span></a>, <a class="ref" href="grfunc_1.html#T13" title="GRFUNC_1:th.13">GRFUNC_1:13</a>, <a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></span>;<br/><a NAME="E24:45_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c23">gg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c21">e</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T12" title="RELAT_1:th.12">RELAT_1:12</a></span>;<br/><a NAME="E25:45_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A24</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c23">gg</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:45_1"><span class="lab"><font color="Green" title="E67">A20</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/><a NAME="E26:45_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c23">gg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:45_1"><span class="lab"><font color="Green" title="E66">A19</font></span></a>, <a class="txt" href="#E22:45_1"><span class="lab"><font color="Green" title="E70">A23</font></span></a>, <a class="ref" href="relat_1.html#T1" title="RELAT_1:th.1">RELAT_1:1</a></span>;<br/><a NAME="E27:45_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c23">gg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>;<br/><a NAME="E28:45_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">gg</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:45_1"><span class="lab"><font color="Green" title="E71">A24</font></span></a>, <a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">ff</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c3">E</font><span class="kw"> such that </span><br/><a NAME="E30:45_1"/><span class="lab"><font color="Green" title="E72">A25</font></span>: 
<font color="Maroon" title="c23">gg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="zf_fund1.html#E24"><span class="lab"><font color="Green" title="E23">Lm11</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:45_1_1"/><span class="lab"><font color="Green" title="E73">A26</font></span>: 
(  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="zf_fund1.html#E16"><span class="lab"><font color="Green" title="E15">Lm3</font></span></a></span>; <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">q</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c25">q</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="c25">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> )</span><br/><span class="kw">assume </span><a NAME="E2:45_1_1"/><span class="lab"><font color="Green" title="E74">A27</font></span>: 
<font color="Maroon" title="c25">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</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"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font></span><br/><a NAME="E3:45_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1_1"><span class="lab"><font color="Green" title="E73">A26</font></span></a>, <a class="txt" href="#E2:45_1_1"><span class="lab"><font color="Green" title="E74">A27</font></span></a>, <a class="ref" href="grfunc_1.html#T15" title="GRFUNC_1:th.15">GRFUNC_1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:45_1"><span class="lab"><font color="Green" title="E72">A25</font></span></a>, <a class="txt" href="#E1:45_1_1"><span class="lab"><font color="Green" title="E73">A26</font></span></a>, <a class="txt" href="#E2:45_1_1"><span class="lab"><font color="Green" title="E74">A27</font></span></a>, <a class="ref" href="grfunc_1.html#T15" title="GRFUNC_1:th.15">GRFUNC_1:15</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/></div><span class="kw">end;</span></div><a NAME="E32:45_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A28</font></span>: 
<font color="Maroon" title="c24">ff</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:45_1"><span class="lab"><font color="Green" title="E69">A22</font></span></a>, <a class="txt" href="zf_fund1.html#E23"><span class="lab"><font color="Green" title="E22">Lm10</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:45_1_2"/><span class="lab"><font color="Green" title="E74">A29</font></span>: 
(  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="zf_fund1.html#E16"><span class="lab"><font color="Green" title="E15">Lm3</font></span></a></span>; <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">q</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c25">q</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="c25">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> )</span><br/><span class="kw">assume </span><a NAME="E2:45_1_2"/><span class="lab"><font color="Green" title="E75">A30</font></span>: 
<font color="Maroon" title="c25">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</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"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font></span><br/><a NAME="E3:45_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1_2"><span class="lab"><font color="Green" title="E74">A29</font></span></a>, <a class="txt" href="#E2:45_1_2"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="ref" href="grfunc_1.html#T15" title="GRFUNC_1:th.15">GRFUNC_1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c20">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_1"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="txt" href="#E9:45_1"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="txt" href="#E11:45_1"><span class="lab"><font color="Green" title="E62">A15</font></span></a>, <a class="txt" href="#E20:45_1"><span class="lab"><font color="Green" title="E68">A21</font></span></a>, <a class="txt" href="#E13:45_1"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E16:45_1"><span class="lab"><font color="Green" title="E65">A18</font></span></a>, <a class="txt" href="#E30:45_1"><span class="lab"><font color="Green" title="E72">A25</font></span></a>, <a class="txt" href="#E1:45_1_2"><span class="lab"><font color="Green" title="E74">A29</font></span></a>, <a class="txt" href="#E2:45_1_2"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="ref" href="grfunc_1.html#T15" title="GRFUNC_1:th.15">GRFUNC_1:15</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/></div><span class="kw">end;</span></div><a NAME="E34:45_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">ff</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:45_1"><span class="lab"><font color="Green" title="E64">A17</font></span></a>, <a class="txt" href="zf_fund1.html#E23"><span class="lab"><font color="Green" title="E22">Lm10</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/><a NAME="E35:45_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A31</font></span>: 
<font color="Maroon" title="c24">ff</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:45_1"><span class="lab"><font color="Green" title="E73">A28</font></span></a>, <a class="ref" href="zf_model.html#T5" title="ZF_MODEL:th.5">ZF_MODEL:5</a></span>;<br/><font color="Maroon" title="c15">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_1"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="txt" href="#E20:45_1"><span class="lab"><font color="Green" title="E68">A21</font></span></a>, <a class="txt" href="#E16:45_1"><span class="lab"><font color="Green" title="E65">A18</font></span></a>, <a class="txt" href="#E30:45_1"><span class="lab"><font color="Green" title="E72">A25</font></span></a>, <a class="ref" href="relat_1.html#T120" title="RELAT_1:th.120">RELAT_1:120</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c24">ff</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T61" title="ZF_LANG1:th.61">ZF_LANG1:61</a></span>
;<br/><span class="kw">hence </span><a NAME="E37:45_1"/>
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:45_1"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</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><span class="kw">end;</span></div>
<a NAME="E14:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A32</font></span>: 
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E15:45"/>
 <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c15">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) or <font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:45_2"/>
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</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="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c3">E</font><span class="kw"> such that </span><br/><a NAME="E3:45_2"/><span class="lab"><font color="Green" title="E57">A33</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:45_2"/><span class="lab"><font color="Green" title="E58">A34</font></span>: 
<font color="Maroon" title="c16">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</a></span>;<br/>
<a NAME="E5:45_2"/>
<font color="Maroon" title="c16">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c6">H9</font>,<font color="Maroon" title="c3">E</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_2"><span class="lab"><font color="Green" title="E58">A34</font></span></a>, <a class="ref" href="zf_model.html#T5" title="ZF_MODEL:th.5">ZF_MODEL:5</a></span>;<br/>
<a NAME="E6:45_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A35</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">z</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="zf_fund1.html#T1" target="_self" title="ZF_FUND1:th.1">Th1</a></span>;<br/>
<a NAME="E8:45_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></span>;<br/>
<a NAME="E9:45_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A36</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T8" title="FUNCT_2:th.8">FUNCT_2:8</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">t</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:45"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="zf_fund1.html#T1" target="_self" title="ZF_FUND1:th.1">Th1</a></span>;<br/>
<a NAME="E11:45_2"/><span class="lab"><font color="Green" title="E61">A37</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T61" title="ZF_LANG1:th.61">ZF_LANG1:61</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c15">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:45_2"><span class="lab"><font color="Green" title="E57">A33</font></span></a>, <a class="ref" href="relat_1.html#T120" title="RELAT_1:th.120">RELAT_1:120</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>
;<br/>
<a NAME="E13:45_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">z</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Maroon" title="c18">t</font>
 
;<br/>
<a NAME="E14:45_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A38</font></span>: 
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:45_2"><span class="lab"><font color="Green" title="E59">A35</font></span></a>, <a class="txt" href="#E9:45_2"><span class="lab"><font color="Green" title="E60">A36</font></span></a></span>;<br/>
<a NAME="E15:45_2"/>
<font color="Maroon" title="c16">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K5" title="ZF_MODEL:func.5">St</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">E</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_2"><span class="lab"><font color="Green" title="E58">A34</font></span></a>, <a class="ref" href="zf_model.html#T5" title="ZF_MODEL:th.5">ZF_MODEL:5</a></span>;<br/>
<a NAME="E16:45_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A39</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D5" target="_self" title="ZF_FUND1:def.5">Def5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c19">x</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="zf_fund1.html#T1" target="_self" title="ZF_FUND1:th.1">Th1</a></span>;<br/>
<a NAME="E18:45_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></span>;<br/>
<a NAME="E19:45_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A40</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T8" title="FUNCT_2:th.8">FUNCT_2:8</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">y</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:45"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="zf_fund1.html#T1" target="_self" title="ZF_FUND1:th.1">Th1</a></span>;<br/>
<font color="Maroon" title="c15">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:45_2"><span class="lab"><font color="Green" title="E57">A33</font></span></a>, <a class="txt" href="#E11:45_2"><span class="lab"><font color="Green" title="E61">A37</font></span></a>, <a class="ref" href="relat_1.html#T120" title="RELAT_1:th.120">RELAT_1:120</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H9</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K5" title="ZF_FUND1:func.5">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c5">H</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>
;<br/>
<a NAME="E22:45_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Maroon" title="c20">y</font>
 
;<br/>
<a NAME="E23:45_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:45_2"><span class="lab"><font color="Green" title="E63">A39</font></span></a>, <a class="txt" href="#E19:45_2"><span class="lab"><font color="Green" title="E64">A40</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:45_2"/>
<font color="Maroon" title="c15">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"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:45_2"><span class="lab"><font color="Green" title="E62">A38</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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><span class="kw">end;</span></div>
<a NAME="E16:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A41</font></span>: 
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">D2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">F2</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:45"><span class="lab"><font color="Green" title="E56">A32</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>;<br/>
<a NAME="E17:45"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="classes2.html#K7" title="CLASSES2:func.7">\/</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">D1</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">F1</font> ) </span> } </span>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E7:45"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E11:45"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="zf_fund1.html#D10" target="_self" title="ZF_FUND1:def.10">Def10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:45"/>
 <a href="zf_fund1.html#K6" title="ZF_FUND1:func.6">Diagram</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c6">H9</font></span>)</span>,<font color="Maroon" title="c3">E</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E12:45"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="txt" href="#E16:45"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="ref" href="zf_fund1.html#T5" target="_self" title="ZF_FUND1:th.5">Th5</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>
