Oh, indeed I was getting confused between those. So as a concrete example of your proof we could consider the following degenerate example case
def f(N: int) -> int:
if N == 0x855bdad365f9331421ab4b13737917cf97b5e8d26246a14c9af1adb060f9724a:
return 1
else:
return 0
def check(x: int, y: float) -> bool:
return f(x) >= y
def argsat(y: float, max_search: int = 2**64) -> int or None:
# We postulate that we have this function because P=NP
if y > 1:
return None
elif y <= 0:
return 0
else:
return 0x855bdad365f9331421ab4b13737917cf97b5e8d26246a14c9af1adb060f9724a
but we could also replace our degenerate f with e.g. sha256.
Oh, indeed I was getting confused between those. So as a concrete example of your proof we could consider the following degenerate example case
but we could also replace our degenerate
fwith e.g.sha256.Is that the gist of your proof sketch?