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Proposition: For proving with knowledge K the goal forall x: G, it suffices to prove G[x <- a] where a is an object constant that does not appear in K and not in G.
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K forall x: G (a not in K union {G})
K G[x <- a]
"We prove (forall x: G). We take an arbitrary (but fixed) constant a and show G[x <- a]."
No knowledge is available about constant yet.