Nuprl Lemma : inf-unique
∀[A:Set(ℝ)]. ∀[b,c:ℝ]. (inf(A) = b ⇒ inf(A) = c ⇒ (b = c))
Proof
Definitions occuring in Statement :
inf: inf(A) = b,
rset: Set(ℝ),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
guard: {T},
inf: inf(A) = b,
lower-bound: lower-bound(A;b)
Lemmas referenced :
rleq_antisymmetry,
inf_wf,
req_witness,
real_wf,
rset_wf,
rleq_inf,
rset-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
universeIsType,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
independent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies
Latex:
\mforall{}[A:Set(\mBbbR{})]. \mforall{}[b,c:\mBbbR{}]. (inf(A) = b {}\mRightarrow{} inf(A) = c {}\mRightarrow{} (b = c))
Date html generated:
2019_10_29-AM-10_40_50
Last ObjectModification:
2019_04_17-PM-04_03_52
Theory : reals
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