Nuprl Lemma : mfun_wf
∀[X,Y:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. (FUN(X ⟶ Y) ∈ Type)
Proof
Definitions occuring in Statement :
mfun: FUN(X ⟶ Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mfun: FUN(X ⟶ Y),
prop: ℙ
Lemmas referenced :
is-mfun_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}[d:metric(X)]. \mforall{}[d':metric(Y)]. (FUN(X {}\mrightarrow{} Y) \mmember{} Type)
Date html generated:
2019_10_30-AM-06_20_57
Last ObjectModification:
2019_10_02-AM-09_57_06
Theory : reals
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