Abstract

We describe an implementation of a pointfree proof of the Alaoglu and the HahnBanach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in "The Hahn-Banach Theorem in Type Theory" [4]. The implementation was partially developed simultaneously with [4] and it was a help in the development of the informal proofs. 1 Introduction We present a machine assisted formalisation of pointfree topology in Martin-Lof's type theory. The continuum and the basic definitions needed in a pointfree approach to functional analysis are given and in this setting we describe implementations of localic formulations of the Alaoglu and the Hahn-Banach theorems. The classical Hahn-Banach theorem says that, if M is a subspace of a normed linear space A and f is a bounded linear functional on M , then f can be extended to a linear functional F on A so that kFk = kfk. (In our proof we use the equivalent formulation: if kfk 1 then f can be extended to F so that kFk 1.) A...

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