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<span class="kw">let </span><font color="Maroon" title="c4">F</font>, <font color="Maroon" title="c5">G</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</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"> ( (  for <font color="Olive" title="b1">r</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <font color="Olive" title="b2">S</font> ) &amp; (  for <font color="Olive" title="b1">r</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <font color="Olive" title="b2">S</font> ) implies <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50_1_2"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 for <font color="Olive" title="b1">r</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <font color="Olive" title="b2">S</font>
 <span class="kw">and </span><br/><a NAME="E2:50_1_2"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
 for <font color="Olive" title="b1">r</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <font color="Olive" title="b2">S</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"> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="50_1_2_1"><span class="kw">now </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">  for <font color="Olive" title="b1">r</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">S</font>)</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">r</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</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">  for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</font></span>)</span> holds  <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Olive" title="b1">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Olive" title="b1">S</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c7">S</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="lmod_7.html#K13" title="LMOD_7:func.13">.</a> <font color="Maroon" title="c3">W</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"> <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">S</font>)</span><br/><span class="kw">thus </span><font color="Maroon" title="c4">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">S</font>) = 
<font color="Maroon" title="c6">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <font color="Maroon" title="c7">S</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_1_2"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c5">G</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">S</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50_1_2"><span class="lab"><font color="Green" title="E21">A3</font></span></a></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:50_1_2"/>
<font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binop_1.html#T2" onmouseover="rs('binop_1/T2')" onmouseout="rh()">BINOP_1:2</a></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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