Nuprl Lemma : locally-non-constant_wf
∀[a,b,c:ℝ]. ∀[f:[a, b] ⟶ℝ]. (locally-non-constant(f;a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
locally-non-constant: locally-non-constant(f;a;b;c),
rfun: I ⟶ℝ,
rccint: [l, u],
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
locally-non-constant: locally-non-constant(f;a;b;c),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
i-member: r ∈ I,
rccint: [l, u],
guard: {T},
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
real_wf,
rleq_wf,
rless_wf,
exists_wf,
rneq_wf,
r-ap_wf,
rccint_wf,
rleq_transitivity,
rfun_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
functionEquality,
hypothesisEquality,
productEquality,
independent_isectElimination,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[a,b,c:\mBbbR{}]. \mforall{}[f:[a, b] {}\mrightarrow{}\mBbbR{}]. (locally-non-constant(f;a;b;c) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-09_24_02
Last ObjectModification:
2015_12_27-PM-11_21_33
Theory : reals
Home
Index