Nuprl Lemma : metric-on-void
∀[X:Type]. Top ⊆r metric(X) supposing ¬X
Proof
Definitions occuring in Statement :
metric: metric(X),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
metric: metric(X),
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x]
Lemmas referenced :
istype-top,
istype-void,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
dependent_set_memberEquality_alt,
functionExtensionality,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
hypothesisEquality,
lambdaFormation_alt,
because_Cache,
independent_pairFormation,
sqequalRule,
productIsType,
functionIsType,
extract_by_obid,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectElimination,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. Top \msubseteq{}r metric(X) supposing \mneg{}X
Date html generated:
2019_10_29-AM-10_51_13
Last ObjectModification:
2019_10_02-AM-09_33_10
Theory : reals
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