Nuprl Lemma : rn-metric-meq
∀[n:ℕ]. ∀[x,y:ℝ^n]. uiff(x ≡ y;req-vec(n;x;y))
Proof
Definitions occuring in Statement :
rn-metric: rn-metric(n),
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
meq: x ≡ y,
nat: ℕ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
rn-metric: rn-metric(n),
meq: x ≡ y,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
real-vec: ℝ^n,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
real-vec-dist-identity,
req_witness,
req_wf,
real-vec-dist_wf,
int-to-real_wf,
req-vec_wf,
real-vec_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
independent_pairFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
hypothesis,
lambdaEquality_alt,
dependent_functionElimination,
applyEquality,
independent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
universeIsType,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. uiff(x \mequiv{} y;req-vec(n;x;y))
Date html generated:
2019_10_30-AM-08_32_16
Last ObjectModification:
2019_10_02-AM-09_45_12
Theory : reals
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