Nuprl Lemma : finite_wf
∀[T:Type]. (finite(T) ∈ ℙ)
Proof
Definitions occuring in Statement :
finite: finite(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
finite: finite(T),
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
equipollent_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
cumulativity,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. (finite(T) \mmember{} \mBbbP{})
Date html generated:
2016_10_21-AM-11_00_06
Last ObjectModification:
2016_08_06-PM-02_33_57
Theory : equipollence!!cardinality!
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