nvdash
Represents logical non-provability or non-derivability in formal logic and mathematical proofs.
Overview
Essential in mathematical logic and proof theory for expressing that a conclusion cannot be derived from given premises or axioms.
- Commonly used in formal logic systems and proof writing
- Appears frequently in papers and texts on mathematical foundations
- Often paired with its positive counterpart \vdash to express provability relationships
- Particularly useful in metamathematics and theoretical computer science when discussing formal systems
Examples
Showing that a logical statement is not derivable in a formal system.
p \land q \nvdash rDemonstrating non-provability in mathematical logic.
\forall x (P(x) \to Q(x)) \nvdash \exists x P(x)Expressing that a set of premises does not entail a conclusion.
\{A, A \to B, B \to C\} \nvdash D