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<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_6.html#D6" target="_self" onmouseover="rs('group_6/D6')" onmouseout="rh()">GROUP_6:def 6</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">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</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">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span><br/>



<a NAME="E1:59_1_1"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>;<br/>
<a NAME="E2:59_1_1"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>;<br/>
<a NAME="E3:59_1_1"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="group_6.html#K6" title="GROUP_6:func.6">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K6" title="GROUP_6:func.6">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D3" target="_self" onmouseover="rs('group_6/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c2">N</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59_1_1"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:59_1_1"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="group_3.html#T9" onmouseover="rs('group_3/T9')" onmouseout="rh()">GROUP_3:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c2">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T106" onmouseover="rs('group_2/T106')" onmouseout="rh()">GROUP_2:106</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font></span>)</span></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c2">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T117" onmouseover="rs('group_3/T117')" onmouseout="rh()">GROUP_3:117</a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c2">N</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T96" onmouseover="rs('group_2/T96')" onmouseout="rh()">GROUP_2:96</a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">N</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T5" target="_self" onmouseover="rs('group_6/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:59_1_1"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="group_2.html#T105" onmouseover="rs('group_2/T105')" onmouseout="rh()">GROUP_2:105</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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