Interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their computations. While some formally verified abstract interpreters have been written in the past, writing and understanding them requires expertise in the use of proof assistants, and requires a non-trivial amount of interactive proofs. This paper presents a formally verified abstract interpreter fully programmed and proved correct in the F* verified programming environment. Thanks to F* refinement types and SMT prover capabilities we demonstrate a substantial saving in proof effort compared to previous works based on interactive proof assistants. Almost all the code of our implementation, proofs included, written in a functional style, are presented directly in the paper.