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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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">  for <font color="Olive" title="b1">M</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">H</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/>  for <font color="Olive" title="b3">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="Olive" title="b1">M</font>  st  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b2">H</font> &amp; <font color="Olive" title="b1">M</font>,<font color="Olive" title="b3">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="Olive" title="b2">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Olive" title="b2">H</font> &amp;  not <font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b2">H</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 holds <br/>(  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp; <font color="Olive" title="b1">M</font>,<font color="Olive" title="b3">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Olive" title="b2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Olive" title="b3">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">  for <font color="Olive" title="b1">H</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/>  for <font color="Olive" title="b2">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="c3">M</font>  st  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="Olive" title="b1">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Olive" title="b1">H</font> &amp;  not <font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 holds <br/>(  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp; <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Olive" title="b1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Olive" title="b1">H</font>,<font color="Olive" title="b2">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Olive" title="b2">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</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">  for <font color="Olive" title="b1">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="c3">M</font>  st  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font> &amp;  not <font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 holds <br/>(  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp; <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Olive" title="b1">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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="c3">M</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"> (  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font> &amp;  not <font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 implies (  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) ) )</span><br/>









<a NAME="E1:15"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<a NAME="E2:15"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">F</font> = <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>);<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:15"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">and </span><br/><a NAME="E4:15"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E5:15"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
 not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">and </span><br/><a NAME="E6:15"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
 not <font color="Maroon" title="c2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">and </span><br/><a NAME="E7:15"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 <span class="kw">and </span><br/><a NAME="E8:15"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3
 <span class="kw">and </span><br/><a NAME="E9:15"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4
 ; <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"> (  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) )</span><br/>

<a NAME="E10:15"/>
( (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> &amp;  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> ) or (  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E11:15"/><span class="kw">then </span>
(  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> or (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T1" target="_self" onmouseover="rs('zfmodel2/T1')" onmouseout="rh()">Th1</a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:15"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>
 ; <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="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp;  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>) )</span><br/>

<a NAME="E13:15"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span> <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">m3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font> holds  <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Olive" title="b1">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">m3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</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"> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span><br/><a NAME="E1:15_1"/>
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">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="c8">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="zf_lang1.html#T71" onmouseover="rs('zf_lang1/T71')" onmouseout="rh()">ZF_LANG1:71</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font><span class="kw"> such that </span><br/><a NAME="E3:15_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T73" onmouseover="rs('zf_lang1/T73')" onmouseout="rh()">ZF_LANG1:73</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c10">f1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</font>);<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1_1"><span class="kw">now </span> <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">m4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font> holds  <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="Olive" title="b1">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">m4</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</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"> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span><br/><a NAME="E1:15_1_1"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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="c11">m4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E2:15_1_1"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K5" title="NUMBERS:func.5">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="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E3:15_1_1"/><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K5" title="NUMBERS:func.5">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"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E4:15_1_1"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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="c11">m4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E5:15_1_1"/><span class="lab"><font color="Green" title="E34">A17</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E6:15_1_1"/><span class="lab"><font color="Green" title="E35">A18</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E7:15_1_1"/><span class="lab"><font color="Green" title="E36">A19</font></span>: 
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="zf_lang1.html#T71" onmouseover="rs('zf_lang1/T71')" onmouseout="rh()">ZF_LANG1:71</a></span>;<br/><div><span class="lab"><font color="Green" title="E37">A20</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><span class="kw">now </span> <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="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span> implies <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>) )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:15_1_1_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 ; <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="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span><br/><a NAME="E2:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15_1_1"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E3:15_1_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E5:15_1_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="zf_model.html#T12" onmouseover="rs('zf_model/T12')" onmouseout="rh()">ZF_MODEL:12</a></span>;<br/><a NAME="E3:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E2:15_1_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E6:15_1_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="zf_model.html#T12" onmouseover="rs('zf_model/T12')" onmouseout="rh()">ZF_MODEL:12</a></span>;<br/><a NAME="E4:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15_1_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="ref" href="zf_model.html#T19" onmouseover="rs('zf_model/T19')" onmouseout="rh()">ZF_MODEL:19</a></span>;<br/><a NAME="E5:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E6:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E13:15"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmodel2.html#T7" target="_self" onmouseover="rs('zfmodel2/T7')" onmouseout="rh()">Th7</a></span>;<br/><a NAME="E7:15_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c2">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font>)</span>)</span> <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> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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> 4</span>)</span>,<font color="Maroon" title="c11">m4</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="zfmodel2.html#T9" target="_self" onmouseover="rs('zfmodel2/T9')" onmouseout="rh()">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E8:15_1_1_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>; <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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1_1_2"><span class="kw">now </span> <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="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>) implies <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span> )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:15_1_1_2"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</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"> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span></span><br/><a NAME="E2:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c2">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font>)</span>)</span> <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> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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> 4</span>)</span>,<font color="Maroon" title="c11">m4</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>;<br/><a NAME="E3:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="zfmodel2.html#T9" target="_self" onmouseover="rs('zfmodel2/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E4:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E13:15"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmodel2.html#T7" target="_self" onmouseover="rs('zfmodel2/T7')" onmouseout="rh()">Th7</a></span>;<br/><a NAME="E5:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E6:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15_1_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="ref" href="zf_model.html#T19" onmouseover="rs('zf_model/T19')" onmouseout="rh()">ZF_MODEL:19</a></span>;<br/><a NAME="E7:15_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E2:15_1_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E6:15_1_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="zf_model.html#T12" onmouseover="rs('zf_model/T12')" onmouseout="rh()">ZF_MODEL:12</a></span>;<br/><span class="kw">hence </span><a NAME="E8:15_1_1_2"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">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#K3" title="ZF_LANG: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#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15_1_1"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E3:15_1_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E5:15_1_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="zf_model.html#T12" onmouseover="rs('zf_model/T12')" onmouseout="rh()">ZF_MODEL:12</a></span>; <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="E10:15_1_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</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="c11">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15_1_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="zf_model.html#T19" onmouseover="rs('zf_model/T19')" onmouseout="rh()">ZF_MODEL:19</a></span>; <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><a NAME="E5:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c9">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T71" onmouseover="rs('zf_lang1/T71')" onmouseout="rh()">ZF_LANG1:71</a></span>;<br/><span class="kw">hence </span><a NAME="E6:15_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">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#T73" onmouseover="rs('zf_lang1/T73')" onmouseout="rh()">ZF_LANG1:73</a></span>; <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="E15:15"/><span class="lab"><font color="Green" title="E29">A21</font></span>: 
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">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#K12" title="ZF_LANG:func.12">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#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">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"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&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#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">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#T71" onmouseover="rs('zf_lang1/T71')" onmouseout="rh()">ZF_LANG1:71</a></span>; <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">  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>)</span><br/>

<a NAME="E16:15"/><span class="lab"><font color="Green" title="E30">A22</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T151" onmouseover="rs('zf_lang1/T151')" onmouseout="rh()">ZF_LANG1:151</a></span>;<br/>
<a NAME="E17:15"/>
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="zfmodel2.html#T2" target="_self" onmouseover="rs('zfmodel2/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<a NAME="E18:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A23</font></span>: 
 not <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E16:15"><span class="lab"><font color="Green" title="E30">A22</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_2.html#D8" onmouseover="rs('funct_2/D8')" onmouseout="rh()">FUNCT_2:def 8</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="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">a9</font> = <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font>;<br/>
<a NAME="E19:15"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c8">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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" onmouseover="rs('zfmodel2/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E20:15"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c8">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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E21:15"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" onmouseover="rs('zfmodel2/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E22:15"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span> <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="c8">a</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> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="zfmodel2.html#T13" target="_self" onmouseover="rs('zfmodel2/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E23:15"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</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> 3</span>)</span>,<font color="Maroon" title="c8">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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:15"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="ref" href="zfmodel2.html#T9" target="_self" onmouseover="rs('zfmodel2/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:15"/>
<span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E15:15"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" onmouseover="rs('zfmodel2/T10')" onmouseout="rh()">Th10</a></span>; <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/>


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