Nuprl Lemma : req-vec-meq-max-metric
∀[n:ℕ]. ∀[v,w:ℝ^n]. v ≡ w supposing req-vec(n;v;w)
Proof
Definitions occuring in Statement :
max-metric: max-metric(n),
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
meq: x ≡ y,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
real-vec: ℝ^n,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
req_witness,
req-vec_wf,
real-vec_wf,
istype-nat,
iff_weakening_uiff,
meq_wf,
max-metric_wf,
meq-max-metric
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
applyEquality,
independent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
universeIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
independent_isectElimination,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[v,w:\mBbbR{}\^{}n]. v \mequiv{} w supposing req-vec(n;v;w)
Date html generated:
2019_10_30-AM-08_42_20
Last ObjectModification:
2019_10_02-AM-11_06_20
Theory : reals
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