Nuprl Lemma : sq_stable__metric-subspace
∀[X:Type]. ∀[d:metric(X)]. ∀[A:Type]. SqStable(metric-subspace(X;d;A))
Proof
Definitions occuring in Statement :
metric-subspace: metric-subspace(X;d;A),
metric: metric(X),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
metric-subspace: metric-subspace(X;d;A),
member: t ∈ T,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
squash: ↓T,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
guard: {T}
Lemmas referenced :
metric_wf,
istype-universe,
strong-subtype-iff-respects-equality,
strong-subtype_wf,
equal-wf,
sq_stable__all,
all_wf,
meq_wf,
sq_stable__implies,
squash_wf,
sq_stable__and,
sq_stable__strong-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
inhabitedIsType,
hypothesisEquality,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
instantiate,
universeEquality,
lambdaFormation_alt,
productElimination,
independent_isectElimination,
independent_functionElimination,
independent_pairFormation,
because_Cache,
sqequalRule,
lambdaEquality_alt,
applyEquality,
functionEquality,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
imageElimination,
axiomEquality,
functionIsTypeImplies,
isect_memberEquality_alt
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[A:Type]. SqStable(metric-subspace(X;d;A))
Date html generated:
2019_10_30-AM-06_30_48
Last ObjectModification:
2019_10_02-AM-10_05_42
Theory : reals
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