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File:StrictContent/ArithmeticAlgebraLogic/forall/rec-forall6
CVS-ID:
Author:Design Science, Inc. (E. Cannon, E. Tabacman, R.Miner)
Description:not (forall s in S . f(s) is in T) = (there exists s in S)

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Created by: webeq

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eq not forall s implies in s suchthat R lambda s in s S in f x T exists s in s S

Source Code:

<math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <csymbol cd="relation1">eq</csymbol>
            <apply>
               <csymbol cd="logic1">not</csymbol>
               <bind>
                  <csymbol cd="quant1">forall</csymbol>
                  <bvar>
                     <ci>s</ci>
                  </bvar>
                  <apply>
                     <csymbol cd="logic1">implies</csymbol>
                     <apply>
                        <csymbol cd="set1">in</csymbol>
                        <ci>s</ci>
                        <apply>
                           <csymbol cd="set1">suchthat</csymbol>
                           <ci>R</ci>
                           <bind>
                              <csymbol cd="fns1">lambda</csymbol>
                              <bvar>
                                 <ci>s</ci>
                              </bvar>
                              <apply>
                                 <csymbol cd="set1">in</csymbol>
                                 <ci>s</ci>
                                 <ci>S</ci>
                              </apply>
                           </bind>
                        </apply>
                     </apply>
                     <apply>
                        <csymbol cd="set1">in</csymbol>
                        <apply>
                           <ci>f</ci>
                           <ci>x</ci>
                        </apply>
                        <ci>T</ci>
                     </apply>
                  </apply>
               </bind>
            </apply>
            <bind>
               <csymbol cd="quant1">exists</csymbol>
               <bvar>
                  <ci>s</ci>
               </bvar>
               <apply>
                  <csymbol cd="set1">in</csymbol>
                  <ci>s</ci>
                  <ci>S</ci>
               </apply>
            </bind>
         </apply>
      </math>