Nuprl Lemma : rfun*_wf
∀[f:ℝ ⟶ ℝ]. ∀[x:ℝ*]. (f*(x) ∈ ℝ*)
Proof
Definitions occuring in Statement :
rfun*: f*(x),
real*: ℝ*,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rfun*: f*(x),
real*: ℝ*,
subtype_rel: A ⊆r B
Lemmas referenced :
real_wf,
nat_wf,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
thin,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectElimination,
because_Cache
Latex:
\mforall{}[f:\mBbbR{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[x:\mBbbR{}*]. (f*(x) \mmember{} \mBbbR{}*)
Date html generated:
2018_05_22-PM-03_15_04
Last ObjectModification:
2017_10_06-PM-02_20_24
Theory : reals_2
Home
Index