Logical assertion

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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.