Nuprl Lemma : retraction_wf
∀[X,A:Type]. ∀[d:metric(X)]. retraction(X;d;A) ∈ Type supposing A ⊆r X
Proof
Definitions occuring in Statement :
retraction: retraction(X;d;A),
metric: metric(X),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
and: P ∧ Q,
retraction: retraction(X;d;A),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
subtype_rel_wf,
meq_wf,
metric-on-subtype,
is-mfun_wf
Rules used in proof :
universeEquality,
instantiate,
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
independent_isectElimination,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
hypothesisEquality,
functionEquality,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,A:Type]. \mforall{}[d:metric(X)]. retraction(X;d;A) \mmember{} Type supposing A \msubseteq{}r X
Date html generated:
2019_10_30-AM-06_36_47
Last ObjectModification:
2019_10_26-PM-00_02_21
Theory : reals
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