proposition: Lemma addℝ_shift_realizer : forall e, addℝ_shift↓e ⊩ ∀x y z ε q, ((x + (y + z)) ε q → ((x + y) + z) ε q)%Re.
proof: Proof. unfold addℝ. Kmove. exists Z. split; [| ok]. Ksolve. Kmove. exists (ε₁ + ε₁0). find. rewrite <- Qcplus_0_l at 1. now apply Qcplus_lt_compat. subst. ring. subst. ring. Kmove. exists ε₁, ε₁0. find. Qed.
imports: QArith Psatz ClassicalRealizability.Kbase ClassicalRealizability.Rationals ClassicalRealizability.Real_definitions ClassicalRealizability.Real_relations