Complete Sequent Calculi for Induction and Infinite Descent
... Any LKID proof can be transformed into a CLKIDω proof. (Proof: We show how to derive any induction rule in CLKIDω .) ...
... Any LKID proof can be transformed into a CLKIDω proof. (Proof: We show how to derive any induction rule in CLKIDω .) ...
Automated Deduction
... It is worthwhile to start these course notes by giving a brief outline of the history of concepts which are fundamental to the area of automated deduction. Even though this outline is quite superficial it nevertheless serves to illustrate how old many of the ideas and concepts at the base of automat ...
... It is worthwhile to start these course notes by giving a brief outline of the history of concepts which are fundamental to the area of automated deduction. Even though this outline is quite superficial it nevertheless serves to illustrate how old many of the ideas and concepts at the base of automat ...
Zvonko Čerin
... As in [16], in each of our sums the lower limit is allowed to vary. Accordingly, we always assume the upper limit to be greater than the lower limit, and that either limit may be negative. In Sections 2-9 we present our results that are collected into eight sets of sums covering the linear sums in S ...
... As in [16], in each of our sums the lower limit is allowed to vary. Accordingly, we always assume the upper limit to be greater than the lower limit, and that either limit may be negative. In Sections 2-9 we present our results that are collected into eight sets of sums covering the linear sums in S ...
Math 713 - hw 2.2 Solutions 2.16a Prove Proposition 2.6 on page 45
... Let x = lim sup xn and y = lim yn . We first assume that x is a real number and use Proposition 2.8(a) to verify that lim sup(xn + yn ) = x + y. Let ε > 0 be given. Since x = lim sup xn there is an N1 ∈ N such that xn ≤ x + ε/2 for all n ≥ N1 . Since yn → y, there is N2 ∈ N such that y − ε/2 < yn < ...
... Let x = lim sup xn and y = lim yn . We first assume that x is a real number and use Proposition 2.8(a) to verify that lim sup(xn + yn ) = x + y. Let ε > 0 be given. Since x = lim sup xn there is an N1 ∈ N such that xn ≤ x + ε/2 for all n ≥ N1 . Since yn → y, there is N2 ∈ N such that y − ε/2 < yn < ...
series with non-zero central critical value
... twists of a particular integral weight newform f . Before stating his results we need to introduce one more bit of notation. If f is a newform of weight 2k and if χ is a Dirichlet character, then fχ is an eigenform for all of the Hecke operators. Hence, by the theory of newforms developed in [1] and ...
... twists of a particular integral weight newform f . Before stating his results we need to introduce one more bit of notation. If f is a newform of weight 2k and if χ is a Dirichlet character, then fχ is an eigenform for all of the Hecke operators. Hence, by the theory of newforms developed in [1] and ...
