Nuprl Lemma : mfun-class_wf
∀[X:Type]. ∀[dx:metric(X)]. ∀[Y:Type]. ∀[dy:metric(Y)]. (mfun-class(X;dx;Y;dy) ∈ Type)
Proof
Definitions occuring in Statement :
mfun-class: mfun-class(X;dx;Y;dy),
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-class: mfun-class(X;dx;Y;dy),
so_lambda: λ2x y.t[x; y],
mfun: FUN(X ⟶ Y),
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
quotient_wf,
mfun_wf,
meqfun_wf,
meqfun-equiv-rel-mfun,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
because_Cache,
setElimination,
rename,
inhabitedIsType,
universeIsType,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[dx:metric(X)]. \mforall{}[Y:Type]. \mforall{}[dy:metric(Y)]. (mfun-class(X;dx;Y;dy) \mmember{} Type)
Date html generated:
2019_10_30-AM-06_33_07
Last ObjectModification:
2019_10_02-AM-10_06_53
Theory : reals
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