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Modal µ-calculus is one of the central languages of logic and verification, whose study involves notoriously complex objects: automata over infinite structures on the model-theoretical side; infinite proofs and proofs by (co)induction on the proof-theoretical side. Nevertheless, axiomatizations have been given for both linear and branching time µ-calculi, with quite involved completeness arguments. We come back to this central problem, considering it from a proof search viewpoint, and providedoi:10.1145/2933575.2933598 dblp:conf/lics/DoumaneBHS16 fatcat:g7cwmr6ddjhitp2xjpmp2sijva