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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font> being   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">BASSIGN</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g1</font>, <font color="Olive" title="b5">g2</font> being   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K49" title="MODELC_1:func.49">BASSModel</a> (<font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">BASSIGN</font>)</span>)</span>  st (  for <font color="Olive" title="b6">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b6">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b4">g1</font> holds <br/><font color="Olive" title="b6">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b5">g2</font> ) holds <br/> for <font color="Olive" title="b6">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b6">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g1</font>) holds <br/><font color="Olive" title="b6">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b5">g2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</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">BASSIGN</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K49" title="MODELC_1:func.49">BASSModel</a> (<font color="Maroon" title="c2">R</font>,<font color="Olive" title="b1">BASSIGN</font>)</span>)</span>  st (  for <font color="Olive" title="b5">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b5">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b3">g1</font> holds <br/><font color="Olive" title="b5">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b4">g2</font> ) holds <br/> for <font color="Olive" title="b5">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b5">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g1</font>) holds <br/><font color="Olive" title="b5">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">g2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">BASSIGN</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</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">f</font>, <font color="Olive" title="b2">g1</font>, <font color="Olive" title="b3">g2</font> being   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K49" title="MODELC_1:func.49">BASSModel</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>)</span>)</span>  st (  for <font color="Olive" title="b4">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b4">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b2">g1</font> holds <br/><font color="Olive" title="b4">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b3">g2</font> ) holds <br/> for <font color="Olive" title="b4">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b4">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g1</font>) holds <br/><font color="Olive" title="b4">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">g2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g1</font>, <font color="Maroon" title="c6">g2</font> be   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K49" title="MODELC_1:func.49">BASSModel</a> (<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>)</span>)</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">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">g1</font> holds <br/><font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">g2</font> ) implies  for <font color="Olive" title="b1">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g1</font>) holds <br/><font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">g2</font>) )</span><br/>







<span class="kw">assume </span><a NAME="E1:160"/><span class="lab"><font color="Green" title="E115">A1</font></span>: 
 for <font color="Olive" title="b1">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">g1</font> holds <br/><font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">g2</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">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g1</font>) holds <br/><font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">g2</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g1</font>) implies <font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">g2</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E2:160"/><span class="lab"><font color="Green" title="E116">A2</font></span>: 
<font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g1</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="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">g2</font>)</span><br/>

<a NAME="E3:160"/><span class="kw">then </span>
<font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K26" title="MODELC_1:func.26">EX</a> <font color="Maroon" title="c5">g1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">pai</font> being    <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E5:160"/><span class="lab"><font color="Green" title="E117">A3</font></span>: 
<font color="Maroon" title="c8">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">and </span><br/><a NAME="E6:160"/><span class="lab"><font color="Green" title="E118">A4</font></span>: 
<font color="Maroon" title="c8">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1 <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T14" target="_self" title="MODELC_1:th.14">Th14</a></span>;<br/>
<a NAME="E7:160"/>
<font color="Maroon" title="c8">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1 <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:160"><span class="lab"><font color="Green" title="E115">A1</font></span></a>, <a class="txt" href="#E6:160"><span class="lab"><font color="Green" title="E118">A4</font></span></a></span>;<br/>
<a NAME="E8:160"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A5</font></span>: 
<font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K26" title="MODELC_1:func.26">EX</a> <font color="Maroon" title="c6">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:160"><span class="lab"><font color="Green" title="E117">A3</font></span></a>, <a class="ref" href="modelc_1.html#T14" target="_self" title="MODELC_1:th.14">Th14</a></span>;<br/>
<a NAME="E9:160"/>
<font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:160"><span class="lab"><font color="Green" title="E116">A2</font></span></a>, <a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:160"/>
<font color="Maroon" title="c7">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">g2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:160"><span class="lab"><font color="Green" title="E119">A5</font></span></a>, <a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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