"could rest assured" is correct and usable in written English.
This phrase is used when you want to give someone assurance or when trying to reassure someone. For example: "You could rest assured that I will keep your secret safe."
VFM He replied that the United States could "rest assured" that China would do so.
But the life force onstage, Mr. Ware could rest assured, was clearly all his.
Audiences could rest assured that the level of wit, storytelling and technical prowess would be incomparably high.
Without this law on the books, Trayvon Martin, the black teenager, might still be alive or, at the very least, we could rest assured that justice would prevail.
If Mr. Bush's torture stained your conscience, you could rest assured that Mr. Obama would not torture (although he might send in a drone to kill instead).
With so many drugs unaccounted for or fraudulently introduced, Courtney could rest assured that it would be nearly impossible to track his dilutions.
Only then, when I had wiped out my first son's entire line, could I rest assured that my kingdom would pass to my second son, the brilliant and talented Duke Gilla-Comgain.
She could now rest assured that what she was projecting to the rest of the world, or to a future partner, reflected her deep inner center.
Now you may be tempted to criticize us or assume that you could do better, but rest assured you're absolutely wrong.
If it seemed the only thing this polymath could not do was play music on a saw, rest assured that he could, and quite well.
If you suspect this is some sort of April Fools' joke, rest assured, we could not possibly make this up.
