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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  =  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,$1);<br/>
<a NAME="E1:155_1_1"/><span class="lab"><font color="Green" title="E110">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> 
 
;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">IT</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a><span class="kw"> such that </span><br/><a NAME="E3:155_1_1"/><span class="lab"><font color="Green" title="E111">A2</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> holds <br/><font color="Maroon" title="c2">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S2" onmouseover="rs('funct_2/S2')" onmouseout="rh()">FUNCT_2:sch 2</a>(<a class="txt" href="#E1:155_1_1"><span class="lab"><font color="Green" title="E110">A1</font></span></a>);<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c3">IT</font> = <font color="Maroon" title="c2">IT</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>) <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T8" onmouseover="rs('funct_2/T8')" onmouseout="rh()">FUNCT_2:8</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">IT</font> = <font color="Maroon" title="c3">IT</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_1.html#K30" title="MODELC_1:func.30">ModelSP</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D40" onmouseover="rs('modelc_1/D40')" onmouseout="rh()">MODELC_1:def 40</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">IT</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">t</font>)</span><br/>

<a NAME="E6:155_1_1"/>
 for <font color="Olive" title="b1">t</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">t</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="155_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c5">IT</font> = <font color="Maroon" title="c4">IT</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">t</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> implies <span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">t</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E2:155_1_1_1"/><span class="lab"><font color="Green" title="E112">A3</font></span>: 
<font color="Maroon" title="c6">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">t</font>)</span><br/>

<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c5">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> = 
<font color="Maroon" title="c5">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D41" onmouseover="rs('modelc_1/D41')" onmouseout="rh()">MODELC_1:def 41</a></span>
<br/>.= 
 <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:155_1_1"><span class="lab"><font color="Green" title="E111">A2</font></span></a>, <a class="txt" href="#E2:155_1_1_1"><span class="lab"><font color="Green" title="E112">A3</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:155_1_1_1"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">t</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:155_1_1"/>
 for <font color="Olive" title="b1">t</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a> holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K31" title="MODELC_1:func.31">Fid</a> (<font color="Maroon" title="c4">IT</font>,<span class="p2">(<span class="default"><a href="modelc_2.html#K25" title="MODELC_2:func.25">Inf_seq</a> <a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K44" title="MODELC_2:func.44">AtomicFunc</a> (<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">t</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
