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<span class="kw">set </span><font color="Maroon" title="c2">A</font> = <span class="p1"><a href="domain_1.html#K13" title="DOMAIN_1:func.13">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K27" title="FOMODEL4:func.27">R3d</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K29" title="FOMODEL4:func.29">R4</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K13" title="DOMAIN_1:func.13">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">B</font> = <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K30" title="FOMODEL4:func.30">R5</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K31" title="FOMODEL4:func.31">R6</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K32" title="FOMODEL4:func.32">R7</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">IT</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K37" title="FOMODEL4:func.37">-rules</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="227_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">P</font> be   <a href="fomodel4.html#NM1" title="FOMODEL4:NM.1">Rule</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="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K37" title="FOMODEL4:func.37">-rules</a>  implies <font color="Maroon" title="c5">P</font> is  <a href="fomodel4.html#V17" title="FOMODEL4:attr.17">Correct</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:227_1_1_1"/>
<font color="Maroon" title="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K37" title="FOMODEL4:func.37">-rules</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="c5">P</font> is  <a href="fomodel4.html#V17" title="FOMODEL4:attr.17">Correct</a> </span><br/><a NAME="E2:227_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K13" title="DOMAIN_1:func.13">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K27" title="FOMODEL4:func.27">R3d</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K29" title="FOMODEL4:func.29">R4</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K13" title="DOMAIN_1:func.13">}</a></span> or <font color="Maroon" title="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K30" title="FOMODEL4:func.30">R5</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K31" title="FOMODEL4:func.31">R6</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K32" title="FOMODEL4:func.32">R7</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:227_1_1_1"/>
<font color="Maroon" title="c5">P</font> is  <a href="fomodel4.html#V17" title="FOMODEL4:attr.17">Correct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:227_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K37" title="FOMODEL4:func.37">-rules</a>  holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#T16" target="_self" title="FOMODEL4:th.16">Th17</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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