Nuprl Lemma : unit-prod_wf
∀[X:Type]. ∀[d:metric(X)]. (I x (X;d) ∈ MetricSpace)
Proof
Definitions occuring in Statement :
unit-prod: I x (X;d),
metric-space: MetricSpace,
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
unit-prod: I x (X;d),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
int_seg: {i..j-},
lelt: i ≤ j < k,
metric-space: MetricSpace
Lemmas referenced :
prod-metric-space_wf,
istype-void,
istype-le,
ifthenelse_wf,
eq_int_wf,
metric-space_wf,
unit-interval-ms_wf,
metric_wf,
int_seg_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
lambdaFormation_alt,
voidElimination,
hypothesis,
hypothesisEquality,
lambdaEquality_alt,
instantiate,
setElimination,
rename,
productElimination,
dependent_pairEquality_alt,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. (I x (X;d) \mmember{} MetricSpace)
Date html generated:
2019_10_29-AM-11_14_16
Last ObjectModification:
2019_10_02-AM-09_54_29
Theory : reals
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