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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b3">G1</font>, <font color="Olive" title="b4">G2</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>  st  <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">F1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b1">F1</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">F2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b2">F2</font> #) &amp;  <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="b3">G1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b3">G1</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="b4">G2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b4">G2</font> #) holds <br/><font color="Olive" title="b3">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">G2</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b2">F2</font></span><br/><b>let </b><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> be  <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>  st  <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">F1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">F1</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="c5">F2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F2</font> #) &amp;  <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">G1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b1">G1</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">G2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Olive" title="b2">G2</font> #) holds <br/><font color="Olive" title="b1">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G2</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F2</font></span><br/><b>let </b><font color="Maroon" title="c6">G1</font>, <font color="Maroon" title="c7">G2</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c4">F1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">F1</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="c5">F2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F2</font> #) &amp;  <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="c6">G1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G1</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="c7">G2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">G2</font> #) implies <font color="Maroon" title="c6">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G2</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F2</font> )</span><br/>





<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E4">A1</font></i>: 
(  <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">F1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">F1</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="c5">F2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F2</font> #) &amp;  <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="c6">G1</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G1</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="c7">G2</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">G2</font> #) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G2</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F2</font></span><br/>

<a NAME="E2:19"/>
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">F1</font> &amp; the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G1</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">F1</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">F1</font> )
 
<b>by </b><i><a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
<font color="Maroon" title="c6">G1</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G2</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F2</font>
 <b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</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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