[isabelle] cardinality



hallo

i have a problem with cardinality.

i don't understand how i have to use card in isabelle.

for example if i try to prove this with card  :
there are 3 natural numbers smaller than 3 

card {(x::nat). x<3} = (3::nat)

is this right or how should i construct this lemma?

another question is where can i find useful lemmas about card? (in set?)

thanks

best regards






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