16

Mouctar Diallo

16. (Preliminary for Th, Feb 22; finalized Sat, March 3) Using only results proven in class or assigned earlier (i.e., don't use induction), show that for all natural numbers x,y, if y<Succ(x), then y≤x.

work | explanation |
---|---|

y < succ(x) | given |

y ε succ(x) | definition of "<" |

y ε U {x,{x}} | definition of succ(x) |

(y ε x) V (y=x) | definition of inclusion |

(y < x) V (y=x) | definition of "<" |

(y ≤ x) | definition of "≤" |

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