Nuprl Lemma : mktopspace_wf
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ]. ∀[equiv:EquivRel(T;x,y.E x y)]. (mktopspace(T;E;equiv) ∈ Space)
Proof
Definitions occuring in Statement :
mktopspace: mktopspace(T;E;equiv),
topspace: Space,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
topspace: Space,
mktopspace: mktopspace(T;E;equiv),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
equiv_rel_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
cumulativity,
functionEquality,
productEquality,
hypothesis,
applyEquality,
lambdaEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[E:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[equiv:EquivRel(T;x,y.E x y)]. (mktopspace(T;E;equiv) \mmember{} Space)
Date html generated:
2018_07_29-AM-09_49_03
Last ObjectModification:
2018_06_21-AM-10_44_11
Theory : inner!product!spaces
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