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<span class="kw">let </span><font color="Maroon" title="c1">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">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">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">M</font><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><br/>  for <font color="Olive" title="b4">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b4">i</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="c1">H</font> holds <br/><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">i</font>,<font color="Olive" title="b2">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></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="Olive" title="b3">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> <font color="Olive" title="b4">i</font></span>)</span>,<font color="Olive" title="b2">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">M</font><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="c2">M</font><br/>  for <font color="Olive" title="b3">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b3">i</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="c1">H</font> holds <br/><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">i</font>,<font color="Olive" title="b1">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></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="Olive" title="b2">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> <font color="Olive" title="b3">i</font></span>)</span>,<font color="Olive" title="b1">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">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">  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="c2">M</font><br/>  for <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b2">i</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="c1">H</font> holds <br/><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></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="Olive" title="b1">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> <font color="Olive" title="b2">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b1">i</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="c1">H</font> holds <br/><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b1">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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"> (  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</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="c1">H</font> implies <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">e</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">b</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>;<br/>
<a NAME="E1:10"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c5">i</font> <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="c5">i</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="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="lab"><font color="Green" title="E11">A2</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</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="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
<br/>.= 
<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</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="zf_fund1.html#T31" onmouseover="rs('zf_fund1/T31')" onmouseout="rh()">ZF_FUND1:31</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</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="zfmisc_1.html#T46" onmouseover="rs('zfmisc_1/T46')" onmouseout="rh()">ZFMISC_1:46</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E12">A3</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T7" onmouseover="rs('grfunc_1/T7')" onmouseout="rh()">GRFUNC_1:7</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p0">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p0">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D3" onmouseover="rs('zf_fund1/D3')" onmouseout="rh()">ZF_FUND1:def 3</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">v</font> <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> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#T32" onmouseover="rs('zf_fund1/T32')" onmouseout="rh()">ZF_FUND1:32</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<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/>
<span class="lab"><font color="Green" title="E13">A4</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
<br/>.= 
<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#T31" onmouseover="rs('zf_fund1/T31')" onmouseout="rh()">ZF_FUND1:31</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#T31" onmouseover="rs('zf_fund1/T31')" onmouseout="rh()">ZF_FUND1:31</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>
;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_4"><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">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_4"/><span class="lab"><font color="Green" title="E14">A5</font></span>: 
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font></span><br/><a NAME="E2:10_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>;<br/><a NAME="E3:10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A6</font></span>: 
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</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="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/><a NAME="E4:10_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><span class="kw"> such that </span><br/><a NAME="E6:10_4"/>
<font color="Maroon" title="c10">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> <font color="Maroon" title="c1">H</font>
 <span class="kw">and </span><br/><a NAME="E7:10_4"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon" title="c9">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#T33" onmouseover="rs('zf_fund1/T33')" onmouseout="rh()">ZF_FUND1:33</a></span>;<br/><a NAME="E8:10_4"/>
 not <font color="Maroon" title="c9">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</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="#E3:10_4"><span class="lab"><font color="Green" title="E15">A6</font></span></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="E9:10_4"/><span class="kw">then </span>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_4"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E10:10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<font color="Maroon" title="c10">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> <font color="Maroon" title="c5">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D3" onmouseover="rs('zf_fund1/D3')" onmouseout="rh()">ZF_FUND1:def 3</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_4"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</a></span>
<br/>.= 
<font color="Maroon" title="c4">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_4"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="zf_fund1.html#T32" onmouseover="rs('zf_fund1/T32')" onmouseout="rh()">ZF_FUND1:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10_4"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_4"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="zf_fund1.html#T32" onmouseover="rs('zf_fund1/T32')" onmouseout="rh()">ZF_FUND1:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E1:10_4"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</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="E6:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p3">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="funct_1.html#T2" onmouseover="rs('funct_1/T2')" onmouseout="rh()">FUNCT_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:10"/>
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</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="c1">H</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"> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span></span><br/>

<a NAME="E8:10"/><span class="kw">then </span>
 <a href="zf_fund1.html#K3" title="ZF_FUND1:func.3">x".</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#T33" onmouseover="rs('zf_fund1/T33')" onmouseout="rh()">ZF_FUND1:33</a></span>;<br/>
<a NAME="E9:10"/><span class="kw">then </span>
<font color="Maroon" title="c5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_fund1.html#D3" onmouseover="rs('zf_fund1/D3')" onmouseout="rh()">ZF_FUND1:def 3</a></span>;<br/>
<a NAME="E10:10"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T45" onmouseover="rs('xboole_1/T45')" onmouseout="rh()">XBOOLE_1:45</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="ref" href="relat_1.html#T78" onmouseover="rs('relat_1/T78')" onmouseout="rh()">RELAT_1:78</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E12:10"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p4">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="zf_fund1.html#K2" title="ZF_FUND1:func.2">decode</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" title="ZF_FUND1:func.4">code</a> <span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c1">H</font></span>)</span></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"> verum</span><br/>


</div>
