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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</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">g1</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/> for <font color="Olive" title="b2">g2</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font>  st <font color="Olive" title="b2">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font> holds <br/>( <font color="Olive" title="b1">g1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b2">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">g1</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</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">g2</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font>  st <font color="Olive" title="b1">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font> holds <br/>( <font color="Maroon" title="c3">g1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b1">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">g2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</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="c4">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</font> implies ( <font color="Maroon" title="c3">g1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c4">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c4">g2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">L1</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="c3">g1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c4">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:41"/>
<font color="Maroon" title="c3">g1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T29" title="FUNCT_2:th.29">FUNCT_2:29</a></span>; <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="c4">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> </span><br/>

<a NAME="E3:41"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">g2</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">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="funct_2.html#T29" title="FUNCT_2:th.29">FUNCT_2:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:41"/>
<font color="Maroon" title="c4">g2</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</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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