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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  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:()"><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">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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  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="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/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:19"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
 <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> #)
 <span class="kw">and </span><br/><a NAME="E2:19"/><span class="lab"><font color="Green" title="E5">A2</font></span>: 
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:19"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</a></span>;<br/>
<a NAME="E4:19"/>
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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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#K2" title="ALTCAT_2:func.2">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:19"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E3:19"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</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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