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### Abstract

We formalize the proofs of two transcendence criteria by J. Hančl
and P. Rucki that assert the transcendence of the sums of certain
infinite series built up by sequences that fulfil certain properties.
Both proofs make use of Roth's celebrated theorem on diophantine
approximations to algebraic numbers from 1955 which we implement as
an assumption without having formalised its proof.