proposition: Lemma growing_infinite : forall un : nat -> nat, (forall n:nat, lt (un n) (un (S n))) -> forall n : nat, le n (un n).
proof: Proof. induction n. - apply Nat.le_0_l. - specialize (H n). unfold lt in H. apply (Nat.le_trans _ (S (un n))). apply le_n_S, IHn. exact H. Qed.
imports: Logic.ConstructiveEpsilon QArith ConstructiveReals ConstructiveAbs ConstructiveMinMax ConstructiveSum ConstructivePower ConstructiveLimits ConstructiveDiagonal ConstructivePartialFunctions CMTbase CMTIntegrableFunctions CMTFullSets CMTPositivity