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Theorem hidingproduct-def

⊦ Πh(IOAut(lstart, lstep, lext), IOAut(rstart, rstep, rext), lren, rren, hideext) = IOAut(Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Πh(lext, rext, lren, rren, hideext))