import PhysicsLogicConsumer.StatePositivity open PhysicsLogicConsumer.StatePositivity example : PhysicsLogicConsumer.StatePositivity.Algebra = (Complex × Complex) := rfl example : distorted.expectation = (1 / 2 + Complex.I) • ContinuousLinearMap.fst Complex Complex Complex + (1 / 2 - Complex.I) • ContinuousLinearMap.snd Complex Complex Complex := rfl example : distorted.groundTerm = 0 := rfl example : mixture.expectation = (1 / 2 : Complex) • ContinuousLinearMap.fst Complex Complex Complex + (1 / 2 : Complex) • ContinuousLinearMap.snd Complex Complex Complex := rfl example : mixture.groundTerm = 0 := rfl example : yes = (1, 0) := rfl