Nuprl Lemma : transparent-nset_wf
∀[K:Type]. (Transparent(K) ∈ ℙ)
Proof
Definitions occuring in Statement :
transparent-nset: Transparent(K),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
exists: ∃x:A. B[x],
uimplies: b supposing a,
nat: ℕ,
guard: {T},
subtype_rel: A ⊆r B,
or: P ∨ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
transparent-nset: Transparent(K),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
less_than_wf,
subtype_rel_transitivity,
istype-nat,
le_wf,
nat_wf,
subtype_rel_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
independent_isectElimination,
intEquality,
rename,
setElimination,
Error :lambdaEquality_alt,
applyEquality,
unionEquality,
functionEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:Type]. (Transparent(K) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-03_02_08
Last ObjectModification:
2019_06_13-AM-11_37_55
Theory : continuity
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