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Aci(s Acl(S assume axiom APS1 axiom PS5 bijection bisection Bourbaki carrier space Chapter completes the proof congruence classes denote partitions denotes the partition episemiomorphism equivalence class exists a unique finite sequences finitistic set following proposition follows by Definition follows by Proposition function with respect functional graph functor given in Fig identity element injection isomorphism LEMMA magma mapping minimalized resolution modular space nonempty nonroot ordered pair partial function Peano space positive natural integer presemiological space given presemiological structure presemlologlcal space prespace prime numbers Proposition 9 proposition holds prosemiomorphism Rci(s Rcl(S relation retractive successor function satisfies axiom semi semicarrier space semiological space semiomorphism semisemiological space sequences that denote singly rooted subset surjection surjective function theorem Theory of Sets total function unique resolution Unq(S whence x e cl(S Y+(X yields zeroed successor function