Nuprl Lemma : sq_stable__regular-int-seq
∀[k:ℕ+]. ∀[f:ℕ+ ⟶ ℤ]. SqStable(k-regular-seq(f))
Proof
Definitions occuring in Statement :
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
regular-int-seq: k-regular-seq(f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
sq_stable__all,
nat_plus_wf,
all_wf,
le_wf,
absval_wf,
subtract_wf,
nat_wf,
sq_stable__le,
less_than'_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
natural_numberEquality,
addEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. SqStable(k-regular-seq(f))
Date html generated:
2016_05_18-AM-06_46_15
Last ObjectModification:
2015_12_28-AM-00_24_54
Theory : reals
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