Nuprl Lemma : metric-eq_wf
∀[X:Type]. ∀[d,d':X ⟶ X ⟶ ℝ]. (metric-eq(X;d;d') ∈ ℙ)
Proof
Definitions occuring in Statement :
metric-eq: metric-eq(X;d;d'),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
metric-eq: metric-eq(X;d;d'),
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
req_wf,
real_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
functionIsType,
universeIsType,
because_Cache,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d,d':X {}\mrightarrow{} X {}\mrightarrow{} \mBbbR{}]. (metric-eq(X;d;d') \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-10_52_15
Last ObjectModification:
2019_10_02-AM-09_34_03
Theory : reals
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