Logical assertion

In mathematical logic, logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. It is equivalent to a sequent with an empty antecedent.

For example, if p = "x is even", the implication

$(\vdash p)\rightarrow (x{\pmod 2}\equiv 0)$

is thus true. We can also write this using the logical assertion symbol, as

$\vdash \left((\vdash p)\rightarrow (x{\pmod 2}\equiv 0)\right)$

In computer programming and programming language semantics, these are used in the form of assertions; one example is a loop invariant.