'proceed with this matter' is correct and usable in written English.
You can use it when you want to express that something needs to be done or continued. For example: "We must proceed with this matter with urgency."
"It's hard for me to understand how the government or how DHS believes the interests of the United States are served by proceeding with this matter," Judge Richard R. Clifton, an appointee of former President George W. Bush, said at last year's hearing.
"There was a settlement that was reached between the parties and we... decided to exercise discretion and not proceed with the matter.
We have involved state and federal regulatory and law enforcement agencies to assist us in determining how to proceed with the matter at hand.
If they're trying to be bossy, thank them for their suggestion but be clear that you are still happy to proceed with the matter in your own way.
Mr. Holder replied, "We intend to proceed with this trial".
"Fifa was not interested in proceeding with the matter," he said.
It's best to proceed with our matter cautiously, with moderation on all sides, so as not to leave open a single loophole, not even a crack.
Dr. Taylor, who has her own line of over-the-counter products, Rx for Brown Skin, advises diligent label reading to avoid irritants, and to proceed with caution no matter the course of action.
Verrilli also argues that the proponents are incorrect in saying that Prop 8 was an attempt to proceed with caution on matters of social policy, noting that the law "amends the California Constitution and permanently bars the legislature from altering the definition of marriage".
"Irrespective of Ahold's decision to proceed in this matter, we are confident with our ownership in ICA," Hakon's chief executive, Claes-Goran Sylven, said in a statement.
