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<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font>, <font color="Maroon" title="c3">C3</font> be   <a href="cat_6.html#V9" title="CAT_6:attr.9">composable</a>   <a href="cat_6.html#V10" title="CAT_6:attr.10">with_identities</a>   <a href="cat_6.html#L1" title="CAT_6:struct.1">CategoryStr</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="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> &amp; <font color="Maroon" title="c2">C2</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font> implies <font color="Maroon" title="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:10"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</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"> (  not <font color="Maroon" title="c2">C2</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font> or <font color="Maroon" title="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:10"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c2">C2</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</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="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_1"/>
( (  not <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c3">C3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) or <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c3">C3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_1_1"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
(  not <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c3">C3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c4">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><span class="kw"> such that </span><br/><a NAME="E3:10_1_1"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
( <font color="Maroon" title="c4">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="cat_7.html#T12" onmouseover="rs('cat_7/T12')" onmouseout="rh()">CAT_7:12</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c5">G</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font><span class="kw"> such that </span><br/><a NAME="E5:10_1_1"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
( <font color="Maroon" title="c5">G</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">G</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="cat_7.html#T12" onmouseover="rs('cat_7/T12')" onmouseout="rh()">CAT_7:12</a></span>;<br/><a NAME="E6:10_1_1"/>
<font color="Maroon" title="c4">F</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c5">G</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1_1"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E5:10_1_1"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E1:10_1_1"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="funct_2.html#T27" onmouseover="rs('funct_2/T27')" onmouseout="rh()">FUNCT_2:27</a></span>;<br/><a NAME="E7:10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">G</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c4">F</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1_1"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E5:10_1_1"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>;<br/><span class="kw">hence </span><a NAME="E8:10_1_1"/>
<font color="Maroon" title="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1_1"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E5:10_1_1"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="cat_6.html#T35" onmouseover="rs('cat_6/T35')" onmouseout="rh()">CAT_6:35</a>, <a class="ref" href="cat_7.html#T12" onmouseover="rs('cat_7/T12')" onmouseout="rh()">CAT_7:12</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_1_2"/>
( <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c3">C3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font></span><br/><div class="add"><a NAME="E2:10_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A6</font></span>: 
( <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c3">C3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="cat_7.html#T15" onmouseover="rs('cat_7/T15')" onmouseout="rh()">CAT_7:15</a></span>;<br/><a NAME="E3:10_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="cat_7.html#T15" onmouseover="rs('cat_7/T15')" onmouseout="rh()">CAT_7:15</a></span>;<br/><span class="kw">hence </span><a NAME="E4:10_1_2"/>
<font color="Maroon" title="c1">C1</font> <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c3">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="cat_7.html#T13" onmouseover="rs('cat_7/T13')" onmouseout="rh()">CAT_7:13</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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