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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">G1</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b3">F2</font>, <font color="Olive" title="b4">G2</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Olive" title="b3">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b4">G2</font> holds <br/>for <font color="Olive" title="b5">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">G1</font><br/> for <font color="Olive" title="b6">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b3">F2</font>,<font color="Olive" title="b4">G2</font><br/> for <font color="Olive" title="b7">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Olive" title="b5">t1</font>,<font color="Olive" title="b6">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b7">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b6">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b7">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">G1</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F2</font>, <font color="Olive" title="b2">G2</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>  st <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">G1</font> &amp; <font color="Olive" title="b1">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">G2</font> holds <br/>for <font color="Olive" title="b3">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">G1</font><br/> for <font color="Olive" title="b4">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F2</font>,<font color="Olive" title="b2">G2</font><br/> for <font color="Olive" title="b5">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">F2</font>, <font color="Maroon" title="c7">G2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">G1</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> implies for <font color="Olive" title="b1">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">G1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> )</span><br/>









<span class="kw">assume </span><a NAME="E1:59"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
( <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">G1</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t1</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">G1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">t1</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">G1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t2</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Olive" title="b1">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">t2</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c10">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c11">s1</font> = <font color="Maroon" title="c8">t1</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">s2</font> = <font color="Maroon" title="c9">t2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<span class="kw">thus </span><span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> = 
<span class="p1"><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K13" title="ISOCAT_2:func.13">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="isocat_2.html#T44" target="_self" title="ISOCAT_2:th.44">Th44</a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c11">s1</font>,<font color="Maroon" title="c12">s2</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="isocat_2.html#D11" target="_self" title="ISOCAT_2:def.11">Def11</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="isocat_2.html#E51"><span class="lab"><font color="Green" title="E38">Lm2</font></span></a></span>
; <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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