lean2/tests/lean/t7.lean

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prelude definition Prop : Type.{1} := Type.{0}
constant and : Prop → Prop → Prop
context
parameter {A : Type} -- Mark A as implicit parameter
parameter R : A → A → Prop
parameter B : Type
definition id (a : A) : A := a
private definition refl : Prop := ∀ (a : A), R a a
definition symm : Prop := ∀ (a b : A), R a b → R b a
definition trans : Prop := ∀ (a b c : A), R a b → R b c → R a c
definition equivalence : Prop := and (and refl symm) trans
end
check id.{2}
check trans.{1}
check symm.{1}
check equivalence.{1}
(*
local env = get_env()
print(env:find("equivalence"):value())
*)