## Two computer-supported proofs in metric space topology (1991)

Venue: | Notices of the American Mathematical Society |

Citations: | 8 - 3 self |

### BibTeX

@ARTICLE{Farmer91twocomputer-supported,

author = {William M. Farmer and F. Javier Thayer},

title = {Two computer-supported proofs in metric space topology},

journal = {Notices of the American Mathematical Society},

year = {1991},

volume = {38},

pages = {38--1133}

}

### OpenURL

### Abstract

Every mathematician will agree that the discovery, analysis, and communication

### Citations

82 | Imps: An interactive mathematical proof system
- Farmer, Guttman, et al.
- 1993
(Show Context)
Citation Context ...e major goal of the system is to provide users with the means to develop machine-checked proofs that are convincing and intelligible to a wide audience. For a detailed overview of the imps system see =-=[6]-=-. In the rest of this section we shall describe three aspects of imps that facilitate the construction of intelligible proofs: its logic, its support for the axiomatic method, and its style of proof. ... |

75 |
A partial functions version of Church’s simple theory of types
- Farmer
- 1990
(Show Context)
Citation Context ...nd the real numbers, respectively. Then the Archimedean principle for the real numbers can be expressed quite naturally as for every a : R for some n : Z asFor more information on the imps logic, see =-=[4, 5, 7]. 2.1-=- Axiomatic Method The axiomatic method comes in two basic styles. There is the \big theory " style in which all reasoning is carried out within one theory|usually some highly expressive theory, s... |

30 |
A Simple Type Theory with Partial Functions and Subtypes
- Farmer
- 1993
(Show Context)
Citation Context ...nd the real numbers, respectively. Then the Archimedean principle for the real numbers can be expressed quite naturally as for every a : R for some n : Z asFor more information on the imps logic, see =-=[4, 5, 7]. 2.1-=- Axiomatic Method The axiomatic method comes in two basic styles. There is the \big theory " style in which all reasoning is carried out within one theory|usually some highly expressive theory, s... |

26 | A theorem prover for a computational logic
- Boyer, Moore
- 1990
(Show Context)
Citation Context ...ogical systems not ordinarily used by mathematicians. Nevertheless, some theorem provers have been used to produce fully machine-checked proofs of mathematically signicant results; for examples, see [=-=1, 2, 3, 8, 9]-=-. In this article we discuss two proofs that were created with the help of a computer theorem proving system called imps (Interactive Mathematical Proof System), which is currently being developed at ... |

15 |
A Proposed Interface Logic for Verification Environments
- Guttman
- 1991
(Show Context)
Citation Context ...e real numbers, respectively. Then the Archimedean principle for the real numbers can be expressed quite naturally as for every a : R for some n : Z a < n. For more information on the imps logic, see =-=[4, 5, 7]-=-. 2.1 Axiomatic Method The axiomatic method comes in two basic styles. There is the “big theory” style in which all reasoning is carried out within one theory—usually some highly expressive theory, su... |

14 |
Automated reasoning about elementary point-set topology
- Wick, McCune
- 1989
(Show Context)
Citation Context ...ogical systems not ordinarily used by mathematicians. Nevertheless, some theorem provers have been used to produce fully machine-checked proofs of mathematically signicant results; for examples, see [=-=1, 2, 3, 8, 9]-=-. In this article we discuss two proofs that were created with the help of a computer theorem proving system called imps (Interactive Mathematical Proof System), which is currently being developed at ... |

10 |
Some Automatic Proofs in Analysis
- Bledsoe
- 1984
(Show Context)
Citation Context ...ogical systems not ordinarily used by mathematicians. Nevertheless, some theorem provers have been used to produce fully machine-checked proofs of mathematically signicant results; for examples, see [=-=1, 2, 3, 8, 9]-=-. In this article we discuss two proofs that were created with the help of a computer theorem proving system called imps (Interactive Mathematical Proof System), which is currently being developed at ... |

9 |
An introduction to Wu’s method for mechanical theorem proving in geometry
- Chou
- 1988
(Show Context)
Citation Context |

8 |
Proof-checking Metamathematics
- Shankar
- 1986
(Show Context)
Citation Context |

7 |
imps: An Interactive
- Farmer, Guttman, et al.
- 1993
(Show Context)
Citation Context ...e major goal of the system is to provide users with the means to develop machine-checked proofs that are convincing and intelligible to a wide audience. For a detailed overview of the imps system see =-=[6]-=-. In the rest of this section we shall describe three aspects of imps that facilitate the construction of intelligible proofs: its logic, its support for the axiomatic method, and its style of proof. ... |

4 |
A proposed interface logic for veri environments
- Guttman
- 1991
(Show Context)
Citation Context ...nd the real numbers, respectively. Then the Archimedean principle for the real numbers can be expressed quite naturally as for every a : R for some n : Z asFor more information on the imps logic, see =-=[4, 5, 7]. 2.1-=- Axiomatic Method The axiomatic method comes in two basic styles. There is the \big theory " style in which all reasoning is carried out within one theory|usually some highly expressive theory, s... |