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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U1</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">partial</a>   <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">non-empty</a>   <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a>   st <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Olive" title="b1">U1</font> holds <br/> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Olive" title="b1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">U1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U1</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">partial</a>   <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">non-empty</a>   <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> implies  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">o</font> =  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font>;<br/>
<span class="kw">assume </span><a NAME="E1:10"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font></span><br/>

<a NAME="E2:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E3:10"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> (<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:10"/>
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="partfun1.html#T47" title="PARTFUN1:th.47">PARTFUN1:47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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