Formalization of Linear Space Theory in the Higher-Order Logic Proving System

Box 1

val s = “s: num_field”;

val membership = “0c IN s ∧ 1c IN s ∧

        !a:complex b:complex. if a IN s ∧ b IN s

        then (a + b IN s) ∧ (a − b IN s) ∧ (a * b IN s) ∧ (if a < > 0 then b/a IN s else a = 0c)

        else F”;