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In this paper we give an arithmetical proof of the strong normalization of lambda-Sym-Prop of Berardi and Barbanera , which can be considered as a formulae-as-types translation of classical propositional logic in natural deduction style. Then we give a translation between the lambda-Sym-Prop-calculus and the lambda-bar-mu-mu-tilde-star-calculus, which is the implicational part of the lambda-bar-mu-mu-tilde-calculus invented by Curien and Herbelin  extended with negation. In this paper wearXiv:1706.07246v1 fatcat:irckjrv6mfedninho6kkivfagm