# Haut PDF The Three Gap Theorem : Specification and Proof in Coq

### The Three Gap Theorem : Specification and Proof in Coq

34

### Specification and Proof of High-Level Functional Properties of Bit-Level Programs

**and**experiments. Stefan Berghofer (Secunet, Germany) is using

**the**sup- port for bit vectors

**in**SPARK, on

**the**big number package of libsparkcrypto ( https: ...discharge

**the**VCs ...

16

### Coq Coq Correct! Verification of Type Checking and Erasure for Coq, in Coq

**Coq**is built around a well-delimited kernel that perfoms typechecking for definitions

**in**a variant of

**the**Calculus of Inductive Constructions ...Although

**the**metatheory of CIC is very ...

29

### CoqIOA : a formalization of IO automata in the Coq proof assistant

**proof**assistant, but

**the**approaches do not support proper compositional ...automata

**in**

**the**Larch Prover [ 11 ], does not support automata composition at ...automata

**specification**...

53

### Implementation of Bourbaki's Elements of Mathematics in Coq: Part Three Structures

**In**this case X = Y

**and**X 0 = Y 0 ...(our

**proof**relies

**in**

**the**fact that 0 = ;, 1 = {0}, 2 = {0, 1}

**and**3 = {0, 1, 2}; but obviously a set with

**three**elements cannot be a ...

119

### Coqoon An IDE for interactive proof development in Coq

**In**

**the**last decade, computer-aided

**proof**development has been gaining mo- ...Interactive

**proof**assistants allow their users to state a mathematical

**theorem**

**in**a ...

18

### A Formal Proof in Coq of LaSalle's Invariance Principle

**the**existence of an equilibrium plays no role

**in**

**the**validity of

**Theorem**...removed

**the**hypothesis F (0) = 0. Still regarding

**the**vector field F ,

**the**assumption “F has ...

18

### The proof-theoretic strength of Ramsey's theorem for pairs and two colors

**and**finitistic reductionism During

**the**early 20th century, mathematics went through a serious foundational crisis, with

**the**discovery of various paradoxes

**and**...e

**and**Brouwer ...

33

### A Formal Proof in Coq of a Control Function for the Inverted Pendulum

**the**notation A `&` B for

**the**intersection of A with B

**and**A !=set0 for exists p, A ...p.

**In**our formalization of

**the**inverted pendulum from Lozano et ...that

**the**set K is ...

15

### A Generic Coq Proof of Typical Worst-Case Analysis

**the**

**specification**

**and**

**the**main correctness

**theorem**; there is no need to look at

**the**

**proof**itself which is ...a

**proof**assistant brings other benefits. Since ...

13

### A Case Study in Formalizing Projective Geometry in Coq: Desargues Theorem

**in**

**the**

**Coq**

**proof**assistant [1, 7]

**and**studies Desargues property both

**in**

**the**plane

**and**

**in**an at least

**three**dimensional setting (noted ≥ ...

36

### Applications of Foundational Proof Certificates in theorem proving

**in**OCaml side by side with a formalization of this MaxChecker

**in**

**Coq**which was restricted to

**the**propositional ...fragment.

**In**extending this treatment to

**the**...

327

### Short proof of Menger's Theorem in Coq (Proof Pearl)

**the**library could profit from some additional cleanup ...conventions

**and**additional documentation), it is already quite usable.

**In**order to establish

**the**library as generally useful, ...

12

### Formalizing Desargues' theorem in Coq using ranks in Coq

**in**iden e re- lations

**in**a 3D setting thanks to ranks

**and**designed an axiom system to apture proje tive geometry using ...Desargues'

**theorem**. We presented

**proof**engineering te ...

7

### Parameterized Specification and Verification of PLC Systems in Coq

**the**

**specification**language they choose is TLA + ...extensively

**in**

**the**field of ...Besides

**the**benefits it brings to

**the**software development, it also helps

**the**formal ...

5

### An Existence Theorem of Nash Equilibrium in Coq and Isabelle

**the**base case were proved independently

**in**[12]

**and**...[11].

**The**fact that

**the**idea behind

**the**

**theorem**emerged

**in**different communities suggests that it is ...

16

### Design of a proof assistant: Coq version 7

**the**new implementation of

**the**system

**Coq**. It ombines

**the**eÆ ien y

**and**safety requirements

**in**a ompletely new design, where

**the**riti al part of

**the**system, ...

9

### A Geometric Proof of Hermite’s Theorem in Function Fields

**the**Galois closure of K over ...not,

**in**general, a geo- metric extension, so there remains some work to be ...be

**the**con- stant field of L. Then, L is a geometric

**and**Galois extension of k ...

16

### A PROOF OF THE CAFFARELLI CONTRACTION THEOREM VIA ENTROPIC REGULARIZATION

**In**

**the**setting of

**Theorem**1, it turns out that much more can be said about

**the**functions f

**and**...explained

**in**

**the**following result, which seems of independent ...

17

### Money Transfer Made Simple: a Specification, a Generic Algorithm, and its Proof

**the**previously cited reliable broadcast algorithms do not use sequence ...represents

**the**current value of p i ’s account. This object provides

**the**processes with two operations denoted balance() ...

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