lean2/tests/lean/run/eq21.lean

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inductive formula :=
eqf : nat → nat → formula,
impf : formula → formula → formula
namespace formula
definition denote : formula → Prop,
denote (eqf n1 n2) := n1 = n2,
denote (impf f1 f2) := denote f1 → denote f2
theorem denote_eqf (n1 n2 : nat) : denote (eqf n1 n2) = (n1 = n2) :=
rfl
theorem denote_impf (f1 f2 : formula) : denote (impf f1 f2) = (denote f1 → denote f2) :=
rfl
end formula