Nuprl Lemma : strong-overt_wf
∀[X:Type]. (sOvert(X) ∈ ℙ')
Proof
Definitions occuring in Statement :
strong-overt: sOvert(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strong-overt: sOvert(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
all_wf,
exists_wf,
Open_wf,
iff_wf,
in-open_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
lambdaEquality,
functionEquality,
productEquality,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:Type]. (sOvert(X) \mmember{} \mBbbP{}')
Date html generated:
2019_10_31-AM-07_19_24
Last ObjectModification:
2015_12_28-AM-11_21_19
Theory : synthetic!topology
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