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...

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

related. Calculus as a unified theory of integration and differentiation started from the conjecture and the proof of the fundamental theorem of calculus. The...

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...

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

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...

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...

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

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

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...

In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and...

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

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

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...

constructive proof of its formal specification. Rocq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions...

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

Lean is a proof assistant and a functional programming language. It is based on the calculus of constructions with inductive types. It is an open-source...

properties a tableau calculus may or may not possess are completeness, destructiveness, and proof confluence. A tableau calculus is called complete if...

In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for...

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

Branch of mathematical logic Visual calculus – Visual mathematical proofs Dunham 1994, p. 120 Weisstein, Eric W. "Proof without Words". MathWorld. Retrieved...

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...

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

Coquand's calculus of constructions (CoC), two calculi in which proofs are regular objects of the discourse and in which one can state properties of proofs the...

In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions...

Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series...

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...

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