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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</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">F</font>, <font color="Olive" title="b2">G</font> being   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>  st (  for <font color="Olive" title="b3">a</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Olive" title="b1">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b3">a</font> ) &amp; (  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> for <font color="Olive" title="b5">f</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> holds  <font color="Olive" title="b1">F</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b5">f</font> ) holds <br/> <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b1">F</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b1">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Olive" title="b2">G</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b2">G</font> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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"> ( (  for <font color="Olive" title="b1">a</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b1">a</font> ) &amp; (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> for <font color="Olive" title="b3">f</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <font color="Maroon" title="c3">F</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b3">f</font> ) implies  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> #) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
 for <font color="Olive" title="b1">a</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Olive" title="b1">a</font>
 <span class="kw">and </span><br/><a NAME="E2:10"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> for <font color="Olive" title="b3">f</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <font color="Maroon" title="c3">F</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Olive" title="b3">f</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">  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> #)</span><br/>

<a NAME="E3:10"/>
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> is  <a href="functor0.html#V1" title="FUNCTOR0:attr.1">Covariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D12" onmouseover="rs('functor0/D12')" onmouseout="rh()">FUNCTOR0:def 12</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">ff</font> being   <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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E5:10"/><span class="lab"><font color="Green" title="E4">A3</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#R8" title="BINOP_1:pred.8">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c5">ff</font>,<font color="Maroon" title="c5">ff</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 ;<br/>
<a NAME="E6:10"/>
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> is  <a href="functor0.html#V1" title="FUNCTOR0:attr.1">Covariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D12" onmouseover="rs('functor0/D12')" onmouseout="rh()">FUNCTOR0:def 12</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">gg</font> being   <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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E8:10"/><span class="lab"><font color="Green" title="E5">A4</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#R8" title="BINOP_1:pred.8">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c6">gg</font>,<font color="Maroon" title="c6">gg</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 ;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">now </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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> holds   the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</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">  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>)</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c10">y</font> = <font color="Maroon" title="c8">b</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> ;<br/><a NAME="E2:10_1"/><span class="lab"><font color="Green" title="E6">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">ff</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:10_1"/><span class="lab"><font color="Green" title="E7">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">gg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E4:10_1"/><span class="lab"><font color="Green" title="E8">A7</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c9">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E2:10_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/><a NAME="E5:10_1"/><span class="lab"><font color="Green" title="E9">A8</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c10">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E2:10_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/><a NAME="E6:10_1"/><span class="lab"><font color="Green" title="E10">A9</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c9">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E3:10_1"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/><a NAME="E7:10_1"/><span class="lab"><font color="Green" title="E11">A10</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c10">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E3:10_1"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/><a NAME="E8:10_1"/><span class="lab"><font color="Green" title="E12">A11</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10_1"><span class="lab"><font color="Green" title="E8">A7</font></span></a></span>;<br/><a NAME="E9:10_1"/><span class="lab"><font color="Green" title="E13">A12</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_1"><span class="lab"><font color="Green" title="E9">A8</font></span></a></span>;<br/><a NAME="E10:10_1"/><span class="lab"><font color="Green" title="E14">A13</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10_1"><span class="lab"><font color="Green" title="E10">A9</font></span></a></span>;<br/><a NAME="E11:10_1"/><span class="lab"><font color="Green" title="E15">A14</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">gg</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_1"><span class="lab"><font color="Green" title="E11">A10</font></span></a></span>;<br/><a NAME="E12:10_1"/><span class="lab"><font color="Green" title="E16">A15</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E2">A1</font></span></a></span>;<br/><a NAME="E13:10_1"/><span class="lab"><font color="Green" title="E17">A16</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E2">A1</font></span></a></span>;<br/><span class="kw">thus </span> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>) = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">b</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="txt" href="#E2:10_1"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>
<br/>.= 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="txt" href="#E3:10_1"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="txt" href="#E8:10_1"><span class="lab"><font color="Green" title="E12">A11</font></span></a>, <a class="txt" href="#E9:10_1"><span class="lab"><font color="Green" title="E13">A12</font></span></a>, <a class="txt" href="#E10:10_1"><span class="lab"><font color="Green" title="E14">A13</font></span></a>, <a class="txt" href="#E11:10_1"><span class="lab"><font color="Green" title="E15">A14</font></span></a>, <a class="txt" href="#E12:10_1"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="txt" href="#E13:10_1"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</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>
<a NAME="E10:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A17</font></span>: 
 the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> <a href="binop_1.html#R8" title="BINOP_1:pred.8">=</a>  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>
 
;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">now </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">  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> 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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> 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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_2"/>
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> 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#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</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">  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:10_2"/><span class="lab"><font color="Green" title="E7">A18</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E4:10_2"/><span class="lab"><font color="Green" title="E8">A19</font></span>: 
<font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">and </span><br/><a NAME="E5:10_2"/><span class="lab"><font color="Green" title="E9">A20</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" onmouseover="rs('zfmisc_1/D2')" onmouseout="rh()">ZFMISC_1:def 2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">x</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c11">y</font> = <font color="Maroon" title="c9">b</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_2"><span class="lab"><font color="Green" title="E7">A18</font></span></a>, <a class="txt" href="#E4:10_2"><span class="lab"><font color="Green" title="E8">A19</font></span></a></span>;<br/><a NAME="E7:10_2"/><span class="lab"><font color="Green" title="E10">A21</font></span>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c11">y</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D18" onmouseover="rs('functor0/D18')" onmouseout="rh()">FUNCTOR0:def 18</a></span>;<br/><a NAME="E8:10_2"/><span class="lab"><font color="Green" title="E11">A22</font></span>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c10">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor0.html#K2" title="FUNCTOR0:func.2">.</a> <font color="Maroon" title="c11">y</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D18" onmouseover="rs('functor0/D18')" onmouseout="rh()">FUNCTOR0:def 18</a></span>;<br/><a NAME="E9:10_2"/><span class="lab"><font color="Green" title="E12">A23</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_2"><span class="lab"><font color="Green" title="E10">A21</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E10:10_2"/><span class="lab"><font color="Green" title="E13">A24</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10_2"><span class="lab"><font color="Green" title="E11">A22</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_2_1"><span class="kw">now </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">  for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> implies <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_2_1"/><span class="lab"><font color="Green" title="E14">A25</font></span>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</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"> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">f</font> = <font color="Maroon" title="c12">z</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font> ;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> = 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Maroon" title="c13">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_2"><span class="lab"><font color="Green" title="E10">A21</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E14">A25</font></span></a>, <a class="ref" href="functor0.html#D15" onmouseover="rs('functor0/D15')" onmouseout="rh()">FUNCTOR0:def 15</a></span>
<br/>.= 
<font color="Maroon" title="c4">G</font> <a href="functor0.html#K5" title="FUNCTOR0:func.5">.</a> <font color="Maroon" title="c13">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E14">A25</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c10">x</font>,<font color="Maroon" title="c11">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10_2"><span class="lab"><font color="Green" title="E11">A22</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E14">A25</font></span></a>, <a class="ref" href="functor0.html#D15" onmouseover="rs('functor0/D15')" onmouseout="rh()">FUNCTOR0:def 15</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><span class="kw">hence </span><a NAME="E12:10_2"/>
 the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E9">A20</font></span></a>, <a class="txt" href="#E9:10_2"><span class="lab"><font color="Green" title="E12">A23</font></span></a>, <a class="txt" href="#E10:10_2"><span class="lab"><font color="Green" title="E13">A24</font></span></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>
<span class="kw">hence </span><a NAME="E12:10"/>
 <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(#  the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>, the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E6">A17</font></span></a>, <a class="ref" href="pboole.html#T3" onmouseover="rs('pboole/T3')" onmouseout="rh()">PBOOLE:3</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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