inductive day :=
monday, tuesday, wednesday, thursday, friday, saturday, sunday

open day

definition next_weekday : day → day,
next_weekday monday    := tuesday,
next_weekday tuesday   := wednesday,
next_weekday wednesday := thursday,
next_weekday thursday  := friday,
next_weekday friday    := monday,
next_weekday saturday  := monday,
next_weekday sunday    := monday

example : next_weekday (next_weekday monday) = wednesday :=
rfl