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<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">x</font>, <font color="Olive" title="b2">y</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font>, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds  <font color="Olive" title="b1">x</font> <a href="binari_2.html#K6" title="BINARI_2:func.6">-</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Olive" title="b2">y</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font>, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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"> <font color="Maroon" title="c2">x</font> <a href="binari_2.html#K6" title="BINARI_2:func.6">-</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c3">y</font></span>)</span></span><br/>



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 for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="binari_2.html#K6" title="BINARI_2:func.6">-</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c3">y</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#D6" target="_self" onmouseover="rs('binari_2/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:24"/>
<font color="Maroon" title="c2">x</font> <a href="binari_2.html#K6" title="BINARI_2:func.6">-</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K2" title="BINARI_2:func.2">Neg2</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#D5" onmouseover="rs('binarith/D5')" onmouseout="rh()">BINARITH:def 5</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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