Nuprl Lemma : image-ap_wf
∀[X,Y:Type]. ∀[d:metric(Y)]. ∀[f:X ⟶ Y]. ∀[x:X]. (f[x] ∈ f[X])
Proof
Definitions occuring in Statement :
image-ap: f[x],
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,
image-space: f[X],
image-ap: f[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
meq_wf,
meq-same
Rules used in proof :
universeEquality,
instantiate,
functionIsType,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
setIsType,
universeIsType,
dependent_set_memberEquality_alt,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
applyEquality,
dependent_pairEquality_alt,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Type]. \mforall{}[d:metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. \mforall{}[x:X]. (f[x] \mmember{} f[X])
Date html generated:
2019_10_30-AM-06_34_48
Last ObjectModification:
2019_10_25-AM-11_20_22
Theory : reals
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