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<span class="kw">reconsider </span><font color="Maroon" title="c3">n</font> = <font color="Maroon" title="c2">n</font> as  non  <a href="xxreal_0.html#NV2" title="XXREAL_0:NV.2">zero</a>   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E27">A1</font></span></a></span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c3">n</font>,   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c3">n</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  = <span class="p1">(<span class="default">$1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> $2</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">n</font>;<br/>
<a NAME="E2:45_1_2"/>
for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c3">n</font></span>)</span>  st ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c3">n</font> holds  <font color="Olive" title="b1">o1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) ) &amp; ( for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c3">n</font> holds  <font color="Olive" title="b2">o2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) ) holds <br/><font color="Olive" title="b1">o1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o2</font>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="binop_2.html#S2" title="BINOP_2:sch.2">BINOP_2:sch 2</a>();<br/></span>
<span class="kw">hence </span><a NAME="E3:45_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c2">n</font></span>)</span>  st ( for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c2">n</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b3">k</font>,<font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Olive" title="b4">l</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font> ) &amp; ( for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c2">n</font> holds  <font color="Olive">b<sub>2</sub></font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b3">k</font>,<font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Olive" title="b4">l</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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