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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</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">f</font> being    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> holds  <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="ringcat1.html#M4" title="RINGCAT1:mode.4">RingMorphism_DOMAIN</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</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"> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="ringcat1.html#M4" title="RINGCAT1:mode.4">RingMorphism_DOMAIN</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font></span><br/>





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 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds  <font color="Olive" title="b1">x</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:49"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="ringcat1.html#M4" title="RINGCAT1:mode.4">RingMorphism_DOMAIN</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ringcat1.html#T13" target="_self" onmouseover="rs('ringcat1/T13')" onmouseout="rh()">Th13</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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