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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a>; <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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</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">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span></span><br/>





<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="o_ring_1.html#D1" onmouseover="rs('o_ring_1/D1')" onmouseout="rh()">O_RING_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T5" onmouseover="rs('realalg2/T5')" onmouseout="rh()">REALALG2:5</a></span>
<br/>.= 
<font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D12" onmouseover="rs('group_1/D12')" onmouseout="rh()">GROUP_1:def 12</a></span>
<br/>.= 
<font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T5" onmouseover="rs('realalg2/T5')" onmouseout="rh()">REALALG2:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_3.html#T65" onmouseover="rs('ring_3/T65')" onmouseout="rh()">RING_3:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#D1" onmouseover="rs('square_1/D1')" onmouseout="rh()">SQUARE_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="o_ring_1.html#D1" onmouseover="rs('o_ring_1/D1')" onmouseout="rh()">O_RING_1:def 1</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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