Nuprl Lemma : strict-upper-bounds_wf
∀[A:Set(ℝ)]. (strict-upper-bounds(A) ∈ Set(ℝ))
Proof
Definitions occuring in Statement : 
strict-upper-bounds: strict-upper-bounds(A)
, 
rset: Set(ℝ)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
strict-upper-bounds: strict-upper-bounds(A)
, 
rset: Set(ℝ)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
strict-upper-bound: A < b
, 
guard: {T}
, 
uimplies: b supposing a
Lemmas referenced : 
strict-upper-bound_wf, 
all_wf, 
real_wf, 
req_wf, 
rless_transitivity1, 
rleq_weakening, 
rset-member_wf, 
set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
setElimination, 
thin, 
rename, 
dependent_set_memberEquality, 
lambdaEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesis, 
hypothesisEquality, 
functionEquality, 
applyEquality, 
because_Cache, 
lambdaFormation, 
dependent_functionElimination, 
independent_functionElimination, 
independent_isectElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
instantiate, 
cumulativity, 
universeEquality
Latex:
\mforall{}[A:Set(\mBbbR{})].  (strict-upper-bounds(A)  \mmember{}  Set(\mBbbR{}))
Date html generated:
2016_05_18-AM-08_11_49
Last ObjectModification:
2015_12_28-AM-01_17_08
Theory : reals
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