proposition: Lemma mulℝ_switch_realizer : forall e, mulℝ_switch↓e ⊩ ∀x y ε q, (x * y)%Re ε q → (y * x)%Re ε q.
proof: Proof. unfold mulℝ at 1. Ksolve. unfold mulℝ. Kmove. exists ε₂, ε₁; find; now rewrite Qcplus_comm || rewrite Qcmult_comm. Qed.
imports: QArith Psatz ClassicalRealizability.Kbase ClassicalRealizability.Rationals ClassicalRealizability.Real_definitions ClassicalRealizability.Real_relations