Nuprl Lemma : in-open_wf
∀[X:Type]. ∀[x:X]. ∀[A:Open(X)]. (x ∈ A ∈ ℙ)
Proof
Definitions occuring in Statement :
in-open: x ∈ A,
Open: Open(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
Open: Open(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
in-open: x ∈ A,
subtype_rel: A ⊆r B
Lemmas referenced :
equal_wf,
Sierpinski_wf,
Sierpinski-top_wf,
subtype-Sierpinski
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x:X]. \mforall{}[A:Open(X)]. (x \mmember{} A \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-07_18_57
Last ObjectModification:
2015_12_28-AM-11_20_52
Theory : synthetic!topology
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