WebCoq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an … Web25 Sep 2024 · This snippet registers a .. coq:: directive, which feeds its contents to Alectryon and displays the resulting responses and goals interleaved with the input and a :coq: role for highlighting inline Coq code. It also replaces the default Pygments highlighter for Coq with Alectryon's improved one, and sets :coq: as the default role.

Standard Library The Coq Proof Assistant - Inria

Web12 Jan 2016 · So the answer would be: Definition mkset {A : Set}: A -> A + A := fun (a : A) := inl a.. Note that, as @Ptival said, Definition set : A -> A + A := fun a => match a with inl l => … Web29 Mar 2015 · Coq definitions. Inductive nat1: Prop := z1 : nat1 s1 : nat1 -> nat1. Inductive nat2 : Set := z2 : nat2 s2 : nat2 -> nat2. Inductive nat3 : Type := z3 : nat3 s3 : nat3 -> … funny hermit crabs

Coq: Prop versus Set in Type (n) - Stack Overflow

WebCoq formalization of set theory. We formalize some basic definitions of sets, functions, ordinal numbers, integers, and cardinal numbers and prove the most commonly used theo-rems in this formal ... Web2 Sep 2024 · SProp is like Prop, but with definitional proof irrelevance, meaning that if p 1, p 2: P then p 1 = p 2. Set is meant for computation. It's predicative, and doesn't have proof irrelevance, which lets you do nice things like not assuming 1 = 2. The Set parts remain during code extraction. Type is a supertype of both of these, allowing you to ... Web6 Oct 2010 · This paper presents a formal system of axiomatic set theory based on the Coq proof assistant and completes the formalization of the basic definitions of sets, functions, … funny hernia