Nuprl Lemma : image-space_wf
∀[X,Y:Type]. ∀[dY:metric(Y)]. ∀[f:X ⟶ Y]. (f[X] ∈ Type)
Proof
Definitions occuring in Statement :
image-space: f[X],
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
exists: ∃x:A. B[x],
image-space: f[X],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
meq_wf
Rules used in proof :
universeEquality,
instantiate,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dY:metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. (f[X] \mmember{} Type)
Date html generated:
2019_10_30-AM-06_34_09
Last ObjectModification:
2019_10_25-AM-11_04_49
Theory : reals
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