Corollary is a statement that follows with little or no proof required from an already proven statement.For example there is a theorem in geometry that the angles opposite to two congruent sides of a triangle are also congruent. A corollary to this statement is that an equilateral triangle is equiangular .
So for a corollary, the proof relies heavily on a given certain theorem .A corollary can be proved but it depends on some theorem heavily. There can't be any assumptions in proof.