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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">M</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> <a href="zfmodel1.html#R1" title="ZFMODEL1:pred.1">is_definable_in</a> <font color="Maroon" title="c1">M</font></span><br/>

<span class="kw">take </span><font color="Maroon" title="c2">H</font> = <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="zfmodel1.html#D3" title="ZFMODEL1:def.3">ZFMODEL1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c2">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:24"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c2">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T63" title="ZF_LANG1:th.63">ZF_LANG1:63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">i</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c1">M</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <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="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">m3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">m4</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span><br/><a NAME="E1:24_1_1_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c5">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T130" title="FUNCT_7:th.130">FUNCT_7:130</a></span>;<br/><a NAME="E2:24_1_1_1"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <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="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a>, <a class="ref" href="zf_lang1.html#T86" title="ZF_LANG1:th.86">ZF_LANG1:86</a></span>;<br/><a NAME="E3:24_1_1_1"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T130" title="FUNCT_7:th.130">FUNCT_7:130</a></span>;<br/><a NAME="E4:24_1_1_1"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a>, <a class="ref" href="zf_lang1.html#T86" title="ZF_LANG1:th.86">ZF_LANG1:86</a></span>;<br/><a NAME="E5:24_1_1_1"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <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="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a>, <a class="ref" href="zf_lang1.html#T86" title="ZF_LANG1:th.86">ZF_LANG1:86</a></span>;<br/><div><span class="lab"><font color="Green" title="E27">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:24_1_1_1_1"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><br/><a NAME="E2:24_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></span>;<br/><span class="kw">hence </span><a NAME="E3:24_1_1_1_1"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E4:24_1_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E2:24_1_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E7:24_1_1_1"/><span class="lab"><font color="Green" title="E28">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">m4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T130" title="FUNCT_7:th.130">FUNCT_7:130</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:24_1_1_1_2"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font></span><br/><a NAME="E2:24_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">m4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E7:24_1_1_1"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></span>;<br/><span class="kw">hence </span><a NAME="E3:24_1_1_1_2"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E4:24_1_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E7:24_1_1_1"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E9:24_1_1_1"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c6">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:24_1_1_1"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="ref" href="zf_model.html#T19" title="ZF_MODEL:th.19">ZF_MODEL:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E2:24_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c5">m3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">ZF_LANG1:80</a></span>;<br/><span class="kw">hence </span><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">m3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T82" title="ZF_LANG1:th.82">ZF_LANG1:82</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E2:24_1"/>
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">ZF_LANG1:80</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:24"/><span class="lab"><font color="Green" title="E22">A9</font></span>: 
<font color="Maroon" title="c1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_model.html#D5" title="ZF_MODEL:def.5">ZF_MODEL:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c4">v</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="c1">M</font>;<br/><span class="kw">let </span><font color="Maroon" title="c5">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">i</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font></span><br/><a NAME="E2:24_2"/><span class="lab"><font color="Green" title="E23">A10</font></span>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T130" title="FUNCT_7:th.130">FUNCT_7:130</a></span>;<br/><a NAME="E3:24_2"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T130" title="FUNCT_7:th.130">FUNCT_7:130</a></span>;<br/><a NAME="E4:24_2"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a>, <a class="ref" href="zf_lang1.html#T86" title="ZF_LANG1:th.86">ZF_LANG1:86</a></span>;<br/><a NAME="E5:24_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c5">a</font></span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c5">a</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_2"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E3:24_2"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></span>;<br/><a NAME="E6:24_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E4:24"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="txt" href="#E4:24_2"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E2:24_2"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E3:24_2"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="zfmodel1.html#D2" title="ZFMODEL1:def.2">ZFMODEL1:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:24_2"/>
<font color="Maroon" title="c3">i</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:24"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K2" title="ZFMODEL1:func.2">def_func</a> <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
