Equivalent formulas to these, written in the language of the Coq interactive theorem prover, are given by Krebbers, Robbert; Spitters, Bas (2013), "Type classes for efficient exact real arithmetic in Coq", Logical Methods in Computer Science, 9 (1): 1:01, 27, arXiv:1106.3448, doi:10.2168/LMCS-9(1:1)2013, MR3029087
O'Connor, Russell (2007), "A monadic, functional implementation of real numbers", Mathematical Structures in Computer Science, 17 (1): 129–159, doi:10.1017/S0960129506005871, MR2311089
Kac, Mark (1959), Statistical Independence in Probability, Analysis and Number Theory, Carus Mathematical Monographs, vol. 12, New York: John Wiley & Sons for the Mathematical Association of America, pp. 2–3, MR0110114
Equivalent formulas to these, written in the language of the Coq interactive theorem prover, are given by Krebbers, Robbert; Spitters, Bas (2013), "Type classes for efficient exact real arithmetic in Coq", Logical Methods in Computer Science, 9 (1): 1:01, 27, arXiv:1106.3448, doi:10.2168/LMCS-9(1:1)2013, MR3029087
Equivalent formulas to these, written in the language of the Coq interactive theorem prover, are given by Krebbers, Robbert; Spitters, Bas (2013), "Type classes for efficient exact real arithmetic in Coq", Logical Methods in Computer Science, 9 (1): 1:01, 27, arXiv:1106.3448, doi:10.2168/LMCS-9(1:1)2013, MR3029087
O'Connor, Russell (2007), "A monadic, functional implementation of real numbers", Mathematical Structures in Computer Science, 17 (1): 129–159, doi:10.1017/S0960129506005871, MR2311089