On Proof-search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-uniication

We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid E-uniication. We show that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-uniiability. This gives us a proof procedure for intuitionistic logic with equality modulo simultaneous rigid E-uniication. We also show that simultaneous rigid E-uniiability is polynomial-time reducible to intuitionistic logic with equality. Thus, any proof procedure for intuitionistic logic with equality can be considered as a procedure for simultaneous rigid E-uniiability. In turn, any procedure for simultaneous rigid E-uniiability gives a procedure for establishing provability in intuitionistic logic with equality. 2 2 in the directory pub/papers/reports. Some reports can be updated, check one of these addresses for the latest version.