Nuprl Lemma : discrete-type_wf
∀[T:Type]. (discrete-type(T) ∈ ℙ)
Proof
Definitions occuring in Statement :
discrete-type: discrete-type(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,
discrete-type: discrete-type(T),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
real_wf,
req_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. (discrete-type(T) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-02_13_13
Last ObjectModification:
2017_10_27-PM-01_12_17
Theory : reals
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