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],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
inject_wf,
surject_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionExtensionality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. (finite'(T) \mmember{} \mBbbP{})
Date html generated:
2016_10_21-AM-10_59_39
Last ObjectModification:
2016_08_06-PM-02_27_39
Theory : equipollence!!cardinality!
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