## Pigeon hole principle (1990)

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Venue: | Journal of Formalized Mathematics |

Citations: | 267 - 13 self |

### BibTeX

@ARTICLE{Trybulec90pigeonhole,

author = {Wojciech A. Trybulec},

title = {Pigeon hole principle},

journal = {Journal of Formalized Mathematics},

year = {1990},

volume = {2},

pages = {4}

}

### Years of Citing Articles

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### Abstract

Summary. We introduce the notion of a predicate that states that a function is one-toone at a given element of its domain (i.e. counterimage of image of the element is equal to its singleton). We also introduce some rather technical functors concerning finite sequences: the lowest index of the given element of the range of the finite sequence, the substring preceding (and succeeding) the first occurrence of given element of the range. At the end of the article we prove the pigeon hole principle.

### Citations

1297 | Functions and their basic properties
- Byliński
- 1990
(Show Context)
Citation Context ...iven element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], =-=[4]-=-, [1], [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and... |

1293 | Tarski Grothendieck set theory
- Trybulec
- 1990
(Show Context)
Citation Context ...) the first occurrence of given element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles =-=[7]-=-, [10], [8], [3], [11], [4], [1], [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, ... |

1229 | Properties of subsets
- Trybulec
- 1990
(Show Context)
Citation Context ... first occurrence of given element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], =-=[10]-=-, [8], [3], [11], [4], [1], [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, ... |

1049 | Functions from a set to a set
- Byliński
- 1990
(Show Context)
Citation Context ...nt of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], [4], [1], =-=[5]-=-, [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and i, k, n a... |

1024 | Relations and their basic properties
- Woronowicz
- 1990
(Show Context)
Citation Context ...e of given element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], =-=[11]-=-, [4], [1], [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets... |

673 | The ordinal numbers
- Bancerek
- 1990
(Show Context)
Citation Context ...element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], [4], =-=[1]-=-, [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and i, k... |

660 | The fundamental properties of natural numbers
- Bancerek
- 1990
(Show Context)
Citation Context ...range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], [4], [1], [5], [6], =-=[2]-=-, and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and i, k, n are natural... |

370 |
Subsets of real numbers
- Trybulec
(Show Context)
Citation Context ... occurrence of given element of the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], =-=[8]-=-, [3], [11], [4], [1], [5], [6], [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y,... |

330 | Finite sets
- Darmochwał
- 1990
(Show Context)
Citation Context ... the range. At the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], [4], [1], [5], =-=[6]-=-, [2], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and i, k, n are na... |

19 |
Non-contiguous substrings and one-to-one finite sequences
- Trybulec
- 1990
(Show Context)
Citation Context ... the end of the article we prove the pigeon hole principle. MML Identifier: FINSEQ_4. WWW: http://mizar.org/JFM/Vol2/finseq_4.html The articles [7], [10], [8], [3], [11], [4], [1], [5], [6], [2], and =-=[9]-=- provide the notation and terminology for this paper. For simplicity, we adopt the following rules: f is a function, p, q are finite sequences, A, B, x, y, z are sets, and i, k, n are natural numbers.... |