lean4-htt/tests/lean/protected_test.lean.expected.out
Leonardo de Moura e9f8f9e5d7 refactor(library/nat): rename nat.le to nat.less_than
Motivation: avoid overload when we use `open nat`.

Unfortunately, we currently do not allow users to mark inductive datatype
declarations as protected.
2016-11-25 18:53:03 -08:00

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protected_test.lean:2:8: error: unknown identifier 'induction_on'
protected_test.lean:3:8: error: unknown identifier 'rec_on'
nat.induction_on : ∀ (n : ), ?M_1 0 → (∀ (a : ), ?M_1 a → ?M_1 (succ a)) → ?M_1 n
less_than.rec_on :
less_than ?M_1 ?M_3 → ?M_2 ?M_1 → (∀ {b : }, less_than ?M_1 b → ?M_2 b → ?M_2 (succ b)) → ?M_2 ?M_3
less_than.rec_on :
less_than ?M_1 ?M_3 → ?M_2 ?M_1 → (∀ {b : }, less_than ?M_1 b → ?M_2 b → ?M_2 (succ b)) → ?M_2 ?M_3
protected_test.lean:8:10: error: unknown identifier 'rec_on'
less_than.rec_on :
less_than ?M_1 ?M_3 → ?M_2 ?M_1 → (∀ {b : }, less_than ?M_1 b → ?M_2 b → ?M_2 (succ b)) → ?M_2 ?M_3