By Su, Hartung, Girod
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Extra resources for A Channel Model for a Watermark Attack
The typing condition requires that initialize has type resultl, law1 has type [result1 F- resulta], and law2 has type [result2 k- resuItu]. Another possible style to describe proofs is characterized by pure composition of inference rules, rather than application of inference rules to an initial axiom. '. '. '. 2. [~- c] \ intro . ' . '. '. '. '. thesis Fig. 7. A proof in Minimal Logic As a difference to the application-oriented style, the intermediate types are inferences between results, rather than just results.
S u c c ( n ) = 1 + n \ transform, add . '. suce( n ) = n + 1 ] base_lemma := mult_def . Ox2=O \ transform, a d d . '. '. LHS = m x 2 + 2 \ unfold(hyp) 9 LHS-=(m+m)+2 \ unfold(succ_lemma) 9 LHS=(m+m)+(I+I) \ l o o p t r a n s f o r m , a d d . '. '. 2. Elements of Proof Design 35 The proof strategy is to proceed by induction: The induction base and the induction step are stated separately in a calculational style and are then used as arguments to the induction rule over naturals. Note the local assumption of the induction hypothesis in the induction step.
Thesis Fig. 7. A proof in Minimal Logic As a difference to the application-oriented style, the intermediate types are inferences between results, rather than just results. In addition, a new operation is introduced, the cut ('o>') of two texts. The purpose of the cut is to compose two texts in a functional way. This is reflected by the following typing rule for the cut: t,... [a ~ b] t~... '. [a ~- c] However, this rule describes a particular situation only. More generally, t2 can have a type of the form Ix : b f- c] in which x occurs fl'ee in c.
A Channel Model for a Watermark Attack by Su, Hartung, Girod