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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">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Olive" title="b2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 holds <br/> for <font color="Olive" title="b3">F</font>, <font color="Olive" title="b4">G</font> being   <a href="polnot_1.html#NM6" title="POLNOT_1:NM.6">Polish-WFF</a> of <font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font> holds <br/> (  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</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">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 holds <br/> for <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being   <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> holds <br/> (  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Olive" title="b1">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Olive" title="b1">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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"> ( <font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies  for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being   <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> holds <br/> (  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:172"/><span class="lab"><font color="Green" title="E95">A1</font></span>: 
<font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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">F</font>, <font color="Olive" title="b2">G</font> being   <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> holds <br/> (  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">F</font>, <font color="Maroon" title="c5">G</font> be   <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>; <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="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">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">set </span><font color="Maroon" title="c7">H</font> =  <a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">K</font> =  <a href="polnot_1.html#K22" title="POLNOT_1:func.22">Polish-operation</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">v</font> = <span class="p1">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>);<br/>
<a NAME="E2:172"/>
( <font color="Maroon" title="c4">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> 1 &amp; <font color="Maroon" title="c5">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> 1 )
 
;<br/>
<a NAME="E3:172"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#T11" target="_self" onmouseover="rs('polnot_1/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c4">F</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">G</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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> <a href="polnot_1.html#K4" title="POLNOT_1:func.4">^^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">E</font> <a href="polnot_1.html#K14" title="POLNOT_1:func.14">.</a> <font color="Maroon" title="c3">t</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:172"><span class="lab"><font color="Green" title="E95">A1</font></span></a></span>;<br/>
<a NAME="E5:172"/>
<span class="p1">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polnot_1.html#K22" title="POLNOT_1:func.22">Polish-operation</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:172"><span class="lab"><font color="Green" title="E95">A1</font></span></a>, <a class="ref" href="polnot_1.html#D28" target="_self" onmouseover="rs('polnot_1/D28')" onmouseout="rh()">Def28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:172"/>
(  <a href="polnot_1.html#K29" title="POLNOT_1:func.29">Polish-WFF-head</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> &amp;  <a href="polnot_1.html#K35" title="POLNOT_1:func.35">Polish-WFF-args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polnot_1.html#K25" title="POLNOT_1:func.25">Polish-binOp</a> (<font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:172"><span class="lab"><font color="Green" title="E95">A1</font></span></a>, <a class="ref" href="polnot_1.html#T64" target="_self" onmouseover="rs('polnot_1/T64')" onmouseout="rh()">Th64</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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