lean4-htt/tests/lean/run/def_brec1.lean
2016-09-20 08:32:37 -07:00

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Text

inductive foo : bool → Type
| Z : foo ff
| O : foo ff → foo tt
| E : foo tt → foo ff
open foo
definition to_nat : ∀ {b}, foo b → nat
| .ff Z := 0
| .tt (O n) := to_nat n + 1
| .ff (E n) := to_nat n + 1
example : to_nat (E (O Z)) = 2 :=
rfl
example : to_nat Z = 0 :=
rfl
example (a : foo ff) : to_nat (O a) = to_nat a + 1 :=
rfl
example (a : foo tt) : to_nat (E a) = to_nat a + 1 :=
rfl