Nuprl Lemma : sq_stable_ex_nonzero
∀n:ℕ. ∀a:ℕn ⟶ ℝ. SqStable(∃i:ℕn. a[i] ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
int-to-real: r(n),
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
sq_stable: SqStable(P),
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uall: ∀[x:A]. B[x],
nat: ℕ
Lemmas referenced :
sq_stable_ex_rneq,
int_seg_wf,
int-to-real_wf,
real_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesis,
because_Cache,
functionEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a:\mBbbN{}n {}\mrightarrow{} \mBbbR{}. SqStable(\mexists{}i:\mBbbN{}n. a[i] \mneq{} r0)
Date html generated:
2017_10_03-AM-09_01_00
Last ObjectModification:
2017_06_16-AM-11_48_16
Theory : reals
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