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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</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="fomodel4.html#NM1" title="FOMODEL4:NM.1">Rule</a> of <font color="Maroon" title="c1">S</font> holds <br/> (  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> is   <a href="fomodel4.html#NM1" title="FOMODEL4:NM.1">Rule</a> of <font color="Maroon" title="c1">S</font> &amp; ( <font color="Olive" title="b1">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> implies <font color="Olive" title="b1">R</font> is  <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">isotone</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</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"> (  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> is   <a href="fomodel4.html#NM1" title="FOMODEL4:NM.1">Rule</a> of <font color="Maroon" title="c1">S</font> &amp; ( <font color="Maroon" title="c2">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> implies <font color="Maroon" title="c2">R</font> is  <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">isotone</a>  ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">Q</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">I</font> =  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> as   <a href="fomodel4.html#NM1" title="FOMODEL4:NM.1">Rule</a> of <font color="Maroon" title="c1">S</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/>
<a NAME="E2:22"/>
 <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">I</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:22"/>
 <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> is   <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="c2">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span> implies <font color="Maroon" title="c2">R</font> is  <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">isotone</a>  )</span><br/>

<div><span class="lab"><font color="Green" title="E11">B0</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">Seqts1</font>, <font color="Maroon" title="c6">Seqts2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></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="c5">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Seqts2</font> implies <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">Seqts2</font> )</span><br/><a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E12">C0</font></span>: 
( <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">Seqts1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Seqts1</font> &amp; <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">Seqts2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Seqts2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T17" title="FUNCT_1:th.17">FUNCT_1:17</a></span>;<br/><span class="kw">assume </span><a NAME="E2:22_1"/>
<font color="Maroon" title="c5">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Seqts2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">Seqts2</font></span><br/><span class="kw">hence </span><a NAME="E3:22_1"/>
<font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">Seqts2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E12">C0</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:22"/>
<font color="Maroon" title="c2">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fomodel2.html#K3" title="FOMODEL2:func.3">id</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></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="c2">R</font> is  <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">isotone</a> </span><br/>

<span class="kw">hence </span><a NAME="E6:22"/>
<font color="Maroon" title="c2">R</font> is  <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">isotone</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E11">B0</font></span></a>, <a class="ref" href="fomodel4.html#D9" target="_self" title="FOMODEL4:def.9">DefMonotonic1</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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