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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_1.html#V2" title="ALTCAT_1:attr.2">transitive</a> <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</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> 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><br/> for <font color="Olive" title="b2">G1</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="c2">B</font>,<font color="Maroon" title="c3">C</font> holds  <font color="Olive" title="b2">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Olive" title="b1">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Olive" title="b1">F1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">F1</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G1</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="c2">B</font>,<font color="Maroon" title="c3">C</font> holds  <font color="Olive" title="b1">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">G1</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="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"> <font color="Maroon" title="c5">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span><br/>









<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p2">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p2">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> = 
<font color="Maroon" title="c5">G1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="functor3.html#T11" target="_self" title="FUNCTOR3:th.11">Th11</a></i>
<br/>.= 
<font color="Maroon" title="c5">G1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T6" title="FUNCTOR2:th.6">FUNCTOR2:6</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T2" title="FUNCTOR2:th.2">FUNCTOR2:2</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="ref" href="functor2.html#T6" title="FUNCTOR2:th.6">FUNCTOR2:6</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:34"/>
<font color="Maroon" title="c5">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
 <b>by </b><i><a class="ref" href="functor2.html#T5" title="FUNCTOR2:th.5">FUNCTOR2:5</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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