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We provide a new sequent calculus that enjoys syntactic cut-elimination andstrongly terminating backward proof search for the intuitionistic Strong L\"oblogic $\sf{iSL}$, an intuitionistic modal logic with a provabilityinterpretation. A novel measure on sequents is used to prove both thetermination of the naive backward proof search strategy, and the admissibilityof cut in a syntactic and direct way, leading to a straightforwardcut-elimination procedure. All proofs have been formalised in the interactivetheorem prover Coq.

A new calculus for intuitionistic Strong L\"ob logic: strong termination and cut-elimination, formalised