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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="polnot_1.html#NM3" title="POLNOT_1:NM.3">Polish-language</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">E</font> being    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">L</font><br/>  for <font color="Olive" title="b2">D</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="b3">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">D</font><br/>  for <font color="Olive" title="b4">K</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>)</span>)</span>,<font color="Olive" title="b2">D</font><br/>  for <font color="Olive" title="b5">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">K</font> is <font color="Olive" title="b3">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Olive" title="b5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>) holds <br/><font color="Olive" title="b4">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b5">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be    <a href="polnot_1.html#M1" title="POLNOT_1:mode.1">Polish-arity-function</a> of <font color="Maroon" title="c1">L</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">D</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">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">K</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>,<font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">K</font> is <font color="Olive" title="b2">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) holds <br/><font color="Olive" title="b3">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">D</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">g</font> being   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">D</font><br/>  for <font color="Olive" title="b2">K</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>,<font color="Maroon" title="c3">D</font><br/>  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">K</font> is <font color="Olive" title="b1">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Olive" title="b3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) holds <br/><font color="Olive" title="b2">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="polnot_1.html#NM7" title="POLNOT_1:NM.7">Polish-recursion-function</a> of <font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">D</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">K</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>,<font color="Maroon" title="c3">D</font><br/>  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">K</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) holds <br/><font color="Olive" title="b1">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">W</font> =  <a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c6">K</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="polnot_1.html#K21" title="POLNOT_1:func.21">Polish-WFF-set</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>,<font color="Maroon" title="c3">D</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">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c6">K</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) holds <br/><font color="Maroon" title="c6">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c7">a</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="c6">K</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a>  &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>) implies <font color="Maroon" title="c6">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:175"/><span class="lab"><font color="Green" title="E96">A1</font></span>: 
<font color="Maroon" title="c6">K</font> is <font color="Maroon" title="c4">g</font> <a href="polnot_1.html#V8" title="POLNOT_1:attr.8">-recursive</a> 
 <span class="kw">and </span><br/><a NAME="E2:175"/><span class="lab"><font color="Green" title="E97">A2</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polnot_1.html#K7" title="POLNOT_1:func.7">Polish-atoms</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</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="c6">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">F</font> = <font color="Maroon" title="c7">a</font> as   <a href="polnot_1.html#NM6" title="POLNOT_1:NM.6">Polish-WFF</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:175"><span class="lab"><font color="Green" title="E97">A2</font></span></a>, <a class="ref" href="polnot_1.html#T34" target="_self" onmouseover="rs('polnot_1/T34')" onmouseout="rh()">Th34</a>, <a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a></span>;<br/>
<a NAME="E4:175"/><span class="lab"><font color="Green" title="E98">A3</font></span>: 
( <font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:175"><span class="lab"><font color="Green" title="E97">A2</font></span></a>, <a class="ref" href="polnot_1.html#T85" target="_self" onmouseover="rs('polnot_1/T85')" onmouseout="rh()">Th85</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c6">K</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> = 
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c8">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <font color="Maroon" title="c8">F</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:175"><span class="lab"><font color="Green" title="E96">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:175"><span class="lab"><font color="Green" title="E98">A3</font></span></a>, <a class="ref" href="binop_1.html#D1" onmouseover="rs('binop_1/D1')" onmouseout="rh()">BINOP_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c4">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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"> verum</span><br/>


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