Nuprl Lemma : open-isect_wf
∀[X:Type]. ∀[A,B:Open(X)]. (open-isect(A;B) ∈ Open(X))
Proof
Definitions occuring in Statement :
open-isect: open-isect(A;B),
Open: Open(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
open-isect: open-isect(A;B),
Open: Open(X),
subtype_rel: A ⊆r B
Lemmas referenced :
sp-meet_wf,
Sierpinski_wf,
Open_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[A,B:Open(X)]. (open-isect(A;B) \mmember{} Open(X))
Date html generated:
2019_10_31-AM-07_18_50
Last ObjectModification:
2015_12_28-AM-11_20_57
Theory : synthetic!topology
Home
Index