lean2/tests/lean/extra/denote_rec.lean

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inductive formula :=
eqf : nat → nat → formula,
andf : formula → formula → formula,
impf : formula → formula → formula,
allf : (nat → formula) → formula
check @formula.rec_on
namespace formula
definition denote : formula → Prop,
denote (eqf n1 n2) := n1 = n2,
denote (andf f1 f2) := denote f1 ∧ denote f2,
denote (impf f1 f2) := denote f1 → denote f2,
denote (allf f) := ∀ n : nat, denote (f n)
end formula
definition denote (f : formula) : Prop :=
formula.rec_on f
(λ n₁ n₂, n₁ = n₂)
(λ f₁ f₂ r₁ r₂, r₁ ∧ r₂)
(λ f₁ f₂ r₁ r₂, r₁ → r₂)
(λ f r, ∀ n : nat, r n)
open formula
eval denote (allf (λ n₁, allf (λ n₂, impf (eqf n₁ n₂) (eqf n₂ n₁))))