Nuprl Lemma : funspace_wf
∀[X,Y:Space]. (funspace(X;Y) ∈ Space)
Proof
Definitions occuring in Statement :
funspace: funspace(X;Y),
topspace: Space,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
topspace: Space,
funspace: funspace(X;Y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
topspace_wf,
equiv_rel_wf,
tfunequiv_wf,
topfuneq_wf,
topfun_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
cumulativity,
functionEquality,
productEquality,
functionExtensionality,
applyEquality,
dependent_functionElimination,
because_Cache,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Space]. (funspace(X;Y) \mmember{} Space)
Date html generated:
2018_07_29-AM-09_48_54
Last ObjectModification:
2018_06_21-AM-10_41_34
Theory : inner!product!spaces
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