What hormone is inhibited by the production of progesterone?

Answers:

Well it inhibites GSK-3 beta. Brain stuff, too long to explain, read more or less it here:

Its effect as a neurosteroid works predominantly through the GSK-3 beta pathway, as an inhibitor. Other GSK-3 beta inhibitors include bipolar mood stabilizers, lithium and valproic acid.

http://en.wikipedia.org/wiki/Progesterone#Neurosteroid

However most folks refer to it regarding reproduction, here's what it does:

Progesterone converts the endometrium to its secretory stage to prepare the uterus for implantation. At matching time progesterone affects the vaginal epithelium and cervical mucus. If pregnancy does not occur, progesterone level will decrease, ascendant, in the human, to menstruation. Normal menstrual bleeding is progesterone subtraction bleeding.

http://en.wikipedia.org/wiki/Progesterone#Reproduction

If I were buried up to my chin in drizzling sand, what would you do to me?

Estrogen is inhibited by the production of progesterone.