proposition: Theorem Rle_proper_realizer : forall e, Rle_proper↓e ⊩ ∀x₁ x₂ y₁ y₂, Total x₁ → Total y₁ → (x₁ ≡ x₂ → y₁ ≡ y₂ → x₁ <= y₁ → x₂ <= y₂)%Re.
proof: Proof. Kmove. apply Rle_trans_realizer. exists x₂, y₁, y₂. repeat split. ok. start. apply Rle_trans_realizer. exists x₂, x₁, y₁. findn 1. eapply sub_term; [| subtyping]. intros π' Hπ'. Kevals. apply Req_sym_realizer. do 2 eexists. split. eapply Ht1. eok. exists ε₁0. find. now eapply sub_term; [| subtyping]. exists ε₁. find. Qed.
imports: QArith Psatz ClassicalRealizability.Kbase ClassicalRealizability.Rationals ClassicalRealizability.Real_definitions