vdash
Represents logical entailment or derivability in mathematical logic and formal proofs.
Overview
Essential in formal logic, proof theory, and mathematical reasoning where it indicates that a conclusion follows from given premises or assumptions.
- Commonly used in sequent calculus and natural deduction systems
- Appears frequently in computer science, particularly in type theory and programming language semantics
- Often combined with other logical symbols to express complex logical relationships
- Used in formal mathematical proofs to show that statements are derivable within a formal system
Examples
Logical deduction or derivation in formal logic.
P \land Q \vdash PFormal proof step showing consequence in mathematical logic.
\forall x(P(x)) \vdash P(a)Sequent calculus notation showing logical entailment.
A, B, C \vdash D \lor E