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etched in stone
Permanently fixed or firmly established; not subject to any amendment or alteration. Often used in the negative. The deal isn't yet etched in stone, but we're confident it will go ahead as hoped.
etch something in(to) somethingand etch something in
to erode a design or message into something, usually with acid. They etched their family crest into their good crystal. He etched in his initials.
See also: etch
cast in stone
Also, etched in stone. Definite, fixed, as in We may choose to stay longer-our plans aren't cast in stone, or When Carl sets an agenda you can safely assume it's etched in stone. Both expressions allude to sculpture, with the first, from the early 1500s, using the verb cast in the sense of pouring and hardening some material into a final form, and the second cutting or corroding a permanent design.