The 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

$(\backslash vdash\; p)\backslash rightarrow(x\; \backslash pmod\; 2\; \backslash equiv\; 0)$

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

$\backslash vdash\; \backslash left(\; (\backslash vdash\; p)\backslash rightarrow(x\; \backslash pmod\; 2\; \backslash equiv\; 0)\; \backslash right)$

Mathematical logic

逻辑断言