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<a NAME="E1:48_1_1"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</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> 
 
<b>by </b><i><a class="ref" href="altcat_2.html#D7" title="ALTCAT_2:def.7">ALTCAT_2:def 7</a></i>;<br/>
<a NAME="E2:48_1_1"/><b>then </b><i><font color="Green" title="E36">A1</font></i>: 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</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">C1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="ref" href="functor0.html#D18" target="_self" title="FUNCTOR0:def.18">Def18</a></i>;<br/>
<b>hence </b><a NAME="E3:48_1_1"/>
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> is <a href="functor0.html#V1" title="FUNCTOR0:attr.1">Covariant</a> &amp; the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> is <a href="functor0.html#V2" title="FUNCTOR0:attr.2">Contravariant</a> )
 <b>by </b><i><a class="ref" href="functor0.html#T16" target="_self" title="FUNCTOR0:th.16">Th16</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D13" target="_self" title="FUNCTOR0:def.13">FUNCTOR0:def 13</a>,<a class="ref" href="functor0.html#D14" target="_self" title="FUNCTOR0:def.14">FUNCTOR0:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font> is <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a></span><br/>

<b>let </b><font color="Maroon" title="c5">o1</font>, <font color="Maroon" title="c6">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D12" target="_self" title="FUNCTOR0:def.12">FUNCTOR0:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</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 the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</font></span>)</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><br/>

<b>assume </b><a NAME="E4:48_1_1"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</font></span>)</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><br/>

<a NAME="E5:48_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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">C1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E6:48_1_1"/><b>then </b>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c3">o</font>
 
<b>by </b><i><a class="txt" href="functor0.html#E2:48_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:48_1_1"/>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">o1</font>,<font color="Maroon" title="c6">o2</font></span>)</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> 
 <b>by </b><i><a class="ref" href="altcat_2.html#D6" title="ALTCAT_2:def.6">ALTCAT_2:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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