Nuprl Lemma : real-sfun_wf
∀[a,b:ℝ]. ∀[f:[a, b] ⟶ℝ]. (real-sfun(f;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
real-sfun: real-sfun(f;a;b),
rfun: I ⟶ℝ,
rccint: [l, u],
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
rfun: I ⟶ℝ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
real-sfun: real-sfun(f;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rccint_wf,
rfun_wf,
rneq_wf,
rleq_wf,
real_wf,
all_wf,
member_rccint_lemma
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_set_memberEquality,
applyEquality,
functionEquality,
rename,
setElimination,
lambdaFormation,
lambdaEquality,
because_Cache,
hypothesisEquality,
productEquality,
setEquality,
isectElimination,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:\mBbbR{}]. \mforall{}[f:[a, b] {}\mrightarrow{}\mBbbR{}]. (real-sfun(f;a;b) \mmember{} \mBbbP{})
Date html generated:
2016_07_08-PM-06_03_02
Last ObjectModification:
2016_07_05-PM-02_50_06
Theory : reals
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