Nuprl Lemma : sq_stable__msep
∀[X:Type]. ∀d:metric(X). ∀x,y:X. SqStable(x # y)
Proof
Definitions occuring in Statement :
msep: x # y,
metric: metric(X),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
msep: x # y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
sq_stable__rless,
int-to-real_wf,
mdist_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
inhabitedIsType,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}d:metric(X). \mforall{}x,y:X. SqStable(x \# y)
Date html generated:
2019_10_29-AM-11_01_04
Last ObjectModification:
2019_10_02-AM-09_42_18
Theory : reals
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