Nuprl Lemma : fun-sep_wf
∀[A:Type]. ∀[ss:SeparationSpace]. ∀[f,g:A ⟶ Point]. (fun-sep(ss;A;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
fun-sep: fun-sep(ss;A;f;g),
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
fun-sep: fun-sep(ss;A;f;g),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-point_wf,
ss-sep_wf,
exists_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
functionExtensionality,
applyEquality,
lambdaEquality,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]. \mforall{}[ss:SeparationSpace]. \mforall{}[f,g:A {}\mrightarrow{} Point]. (fun-sep(ss;A;f;g) \mmember{} \mBbbP{})
Date html generated:
2016_11_08-AM-09_11_47
Last ObjectModification:
2016_11_02-AM-10_23_26
Theory : inner!product!spaces
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