Nuprl Lemma : strong-regular-int-seq_wf
∀[a,b:ℤ]. ∀[f:ℕ+ ⟶ ℤ]. (strong-regular-int-seq(a;b;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
strong-regular-int-seq: strong-regular-int-seq(a;b;f),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strong-regular-int-seq: strong-regular-int-seq(a;b;f),
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_plus_wf,
le_wf,
absval_wf,
subtract_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
multiplyEquality,
hypothesisEquality,
setElimination,
rename,
applyEquality,
functionExtensionality,
addEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. \mforall{}[f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (strong-regular-int-seq(a;b;f) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-07_12_54
Last ObjectModification:
2017_09_20-PM-04_57_13
Theory : reals
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