Nuprl Lemma : const-nonzero-on
∀[I:Interval]. ∀a:ℝ. (a ≠ r0 ⇒ a≠r0 for x ∈ I)
Proof
Definitions occuring in Statement :
nonzero-on: f[x]≠r0 for x ∈ I,
interval: Interval,
rneq: x ≠ y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
nonzero-on: f[x]≠r0 for x ∈ I,
sq_exists: ∃x:{A| B[x]},
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rabs_wf,
rabs-neq-zero,
rleq_weakening,
req_weakening,
i-member_wf,
i-approx_wf,
real_wf,
and_wf,
rless_wf,
int-to-real_wf,
all_wf,
rleq_wf,
set_wf,
nat_plus_wf,
icompact_wf,
rneq_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_set_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
because_Cache,
independent_isectElimination,
setElimination,
rename,
natural_numberEquality,
sqequalRule,
lambdaEquality,
functionEquality
Latex:
\mforall{}[I:Interval]. \mforall{}a:\mBbbR{}. (a \mneq{} r0 {}\mRightarrow{} a\mneq{}r0 for x \mmember{} I)
Date html generated:
2016_05_18-AM-09_19_04
Last ObjectModification:
2015_12_27-PM-11_24_15
Theory : reals
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