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<a NAME="E1:63_1_1"/><span class="lab"><font color="Green" title="E25">H</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">r</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">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D5" target="_self" onmouseover="rs('field_5/D5')" onmouseout="rh()">defr</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">e</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">o</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_1"><span class="lab"><font color="Green" title="E25">H</font></span></a>, <a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/>
<span class="kw">take </span>
 <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #)
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> &amp;  the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E4:63_1_1"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font> &amp;  the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> &amp;  the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_5.html#K5" title="FIELD_5:func.5">ren_mult</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c5">o</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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