In mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Formal language: The set...

In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a...

actually closely related. From the conjecture and the proof of the fundamental theorem of calculus, calculus as a unified theory of integration and differentiation...

has proved very important in proof theory. Gentzen (1934) further introduced the idea of the sequent calculus, a calculus advanced in a similar spirit...

predicates Proof calculus, a framework for expressing systems of logical inference Sequent calculus, a proof calculus for first-order logic Cirquent calculus, a...

the calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has...

we can reliably find proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction...

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to...

and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements...

and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive...

derivatives. The calculus has applications in, for example, stochastic filtering. Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's...

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...

normalization of the underlying calculus if there is one) implies the consistency of the calculus: since there is no cut-free proof of falsity, there is no contradiction...

The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

for several proof calculi there is an accepted notion. For example: In Gerhard Gentzen's natural deduction calculus the analytic proofs are those in...

distinguishes proof nets from regular proof calculi such as the natural deduction calculus and the sequent calculus, where these phenomena are present. Proof nets...

standard semantics does not admit an effective, sound, and complete proof calculus. The model-theoretic properties of HOL with standard semantics are also...

called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns...

computation known as lambda calculus. The Curry–Howard correspondence is the observation that there is an isomorphism between the proof systems, and the models...

The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs are those that are cut-free...

specification. Coq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions. Coq is not an automated...

its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational...

outline should not be considered a rigorous proof of the theorem. We work with first-order predicate calculus. Our languages allow constant, function and...

system based on the Calculus of Inductive Constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on...

This is a list of calculus topics. Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation...

Retoré's calculus, BV, in which the two noncommutative operations are collapsed onto a single, self-dual, operator, and proposed a novel proof calculus, the...

judgement that possesses a proof in the sequent calculus making use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use...

Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...

as foundations are: Typed λ-calculus of Alonzo Church Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory...