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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of 2,<a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ) <b>-&gt; </b>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  = <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default">$1 <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default">$1 <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span>);<br/>
<b>consider </b><font color="Maroon" title="c1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> , <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> <b> such that </b><br/><a NAME="E2:26_1"/><i><font color="Green" title="E11">A1</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of 2,<a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  holds  <font color="Maroon" title="c1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></i>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span>
<div class="add"><b>take </b><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  holds  <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.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">x</font>,<font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)</span><br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.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="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)</span><br/><b>reconsider </b><font color="Maroon" title="c5">a</font> = <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> as   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of 2,<a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T121" title="FINSEQ_2:th.121">FINSEQ_2:121</a></i>;<br/><b>thus </b><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.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="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> = 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span>)
<b>by </b><i><a class="txt" href="#E2:26_1"><i><font color="Green" title="E11">A1</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span>)
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>)
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>


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