Nuprl Lemma : rrange_wf
∀[I:Interval]. ∀[f:I ⟶ℝ]. (f[x](x∈I) ∈ Set(ℝ))
Proof
Definitions occuring in Statement :
rrange: f[x](x∈I),
rfun: I ⟶ℝ,
interval: Interval,
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T
Definitions unfolded in proof :
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rrange: f[x](x∈I),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
so_apply: x[s],
rfun: I ⟶ℝ,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x]
Lemmas referenced :
req_transitivity,
i-member_wf,
req_wf,
real_wf,
all_wf,
rfun_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
because_Cache,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
hypothesis,
independent_pairFormation,
lemma_by_obid,
isectElimination,
applyEquality,
independent_isectElimination,
productEquality,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. (f[x](x\mmember{}I) \mmember{} Set(\mBbbR{}))
Date html generated:
2016_05_18-AM-09_08_16
Last ObjectModification:
2015_12_27-PM-11_31_23
Theory : reals
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