Nuprl Lemma : open-union_wf
∀[X:Type]. ∀[A:ℕ ⟶ Open(X)]. (open-union(n.A[n]) ∈ Open(X))
Proof
Definitions occuring in Statement :
open-union: open-union(n.A[n]),
Open: Open(X),
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
open-union: open-union(n.A[n]),
Open: Open(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
sp-lub_wf,
Open_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[A:\mBbbN{} {}\mrightarrow{} Open(X)]. (open-union(n.A[n]) \mmember{} Open(X))
Date html generated:
2019_10_31-AM-07_18_54
Last ObjectModification:
2015_12_28-AM-11_20_55
Theory : synthetic!topology
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