lean2/tests/lean/urec.lean

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Text

import data.nat data.examples.vector data.list.basic
attribute nat [recursor]
attribute nat.rec [recursor]
attribute nat.rec_on [recursor]
attribute nat.strong_induction_on [recursor]
attribute nat.cases_on [recursor]
attribute vector.cases_on [recursor]
attribute vector.brec_on [recursor]
axiom badrec1 : Π (A : Type) (C : A → Type) (a : A) (l : list A), C a
attribute badrec1 [recursor]
axiom badrec2 : Π (A : Type) (M : list A → Type) (l : list A) (a : nat), M l
attribute badrec2 [recursor]
open list
axiom myrec : Π (A : Type) (M : list A → Type) (l : list A), M [] → (∀ a, M [a]) → (∀ a₁ a₂, M [a₁, a₂]) → M l
attribute myrec [recursor]
set_option pp.implicit true
set_option pp.universes true
check @myrec
print [recursor] myrec
print [recursor] nat.induction_on
check @vector.induction_on
print [recursor] vector.induction_on
check @Exists.rec
print [recursor] Exists.rec