fact: Definition addℝ_proper := λ"eqx" λ"eqy" λ"ε₁" λ"ε₂" λ"q₁" λ"q₂" λ"XY₁" λ"XY₂" "XY₁" @ (λ"ε₁₁" λ"ε₁₂" λ"q₁₁" λ"q₁₂" λ"X₁" λ"Y₁" "XY₂" @ (λ"ε₂₁" λ"ε₂₂" λ"q₂₁" λ"q₂₂" λ"X₂" λ"Y₂" ("eqx" @ "ε₁₁" @ "ε₂₁" @ "q₁₁" @ "q₂₁" @ "X₁" @ "X₂") @ ("eqy" @ "ε₁₂" @ "ε₂₂" @ "q₁₂" @ "q₂₂" @ "Y₁" @ "Y₂"))).
imports: QArith Psatz ClassicalRealizability.Kbase ClassicalRealizability.Rationals ClassicalRealizability.Real_definitions ClassicalRealizability.Real_relations