proposition: Theorem ev_sum : forall n m, ev n -> ev m -> ev (n + m).
proof: Proof. Admitted. Inductive ev' : nat -> Prop := | ev'_0 : ev' 0 | ev'_2 : ev' 2 | ev'_sum : forall n m, ev' n -> ev' m -> ev' (n + m). Theorem ev'_ev : forall n, ev' n <-> ev n. Proof. Admitted. Theorem ev_ev__ev : forall n m, ev (n+m) -> ev n -> ev m. Proof. Admitted. Theorem ev_plus_plus : forall n m p, ev (n+m) -> ev (n+p) -> ev (m+p). Proof. Admitted. Module Playground. Inductive le : nat -> nat -> Prop := | le_n : forall n, le n n | le_S : forall n m, (le n m) -> (le n (S m)). Notation "m <= n" := (le m n). Theorem test_le1 : 3 <= 3. Proof. apply le_n. Qed.
imports: Logic