Nuprl Lemma : rexp-approx_wf
∀[x:ℝ]. ∀[k:ℕ]. ∀[N:ℕ+]. (rexp-approx(x;k;N) ∈ ℤ)
Proof
Definitions occuring in Statement :
rexp-approx: rexp-approx(x;k;N),
real: ℝ,
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rexp-approx: rexp-approx(x;k;N),
subtype_rel: A ⊆r B
Lemmas referenced :
poly-approx_wf,
int-rdiv_wf,
fact_wf,
nat_plus_inc_int_nzero,
int-to-real_wf,
nat_plus_wf,
istype-nat,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
hypothesis,
applyEquality,
natural_numberEquality,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[k:\mBbbN{}]. \mforall{}[N:\mBbbN{}\msupplus{}]. (rexp-approx(x;k;N) \mmember{} \mBbbZ{})
Date html generated:
2019_10_29-AM-10_38_52
Last ObjectModification:
2019_02_03-PM-09_51_42
Theory : reals
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