Nuprl Lemma : rfun-ap_wf
∀[f:ℝ ⟶ ℝ]. ∀[x:ℝ]. (f(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
rfun-ap: f(x),
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-ap: f(x)
Lemmas referenced :
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
functionExtensionality,
hypothesisEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
functionEquality
Latex:
\mforall{}[f:\mBbbR{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[x:\mBbbR{}]. (f(x) \mmember{} \mBbbR{})
Date html generated:
2017_10_04-PM-11_02_08
Last ObjectModification:
2017_06_30-PM-03_18_04
Theory : reals_2
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