Nuprl Definition : VesleySchema2
VesleySchema2 ==
∀P:(ℕ+ ⟶ ℤ) ⟶ ℙ
((∀f:ℕ+ ⟶ ℤ. ∀k:ℕ+. ∃g:{x:ℕ+ ⟶ ℤ| ¬(P x)} . (g = regularize(1;f) ∈ (ℕ+k ⟶ ℤ)))
⇒ (∀Q:{x:ℕ+ ⟶ ℤ| ¬(P x)} ⟶ 𝔹. ∃Q':(ℕ+ ⟶ ℤ) ⟶ 𝔹. ∀x:{x:ℕ+ ⟶ ℤ| ¬(P x)} . Q' x = Q x))
Definitions occuring in Statement :
regularize: regularize(k;f),
int_seg: {i..j-},
nat_plus: ℕ+,
bool: 𝔹,
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions occuring in definition :
apply: f a,
bool: 𝔹,
equal: s = t ∈ T,
not: ¬A,
int: ℤ,
nat_plus: ℕ+,
function: x:A ⟶ B[x],
set: {x:A| B[x]} ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
natural_number: $n,
regularize: regularize(k;f),
int_seg: {i..j-},
implies: P ⇒ Q,
prop: ℙ
FDL editor aliases :
VesleySchema2
Latex:
VesleySchema2 ==
\mforall{}P:(\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}) {}\mrightarrow{} \mBbbP{}
((\mforall{}f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. \mforall{}k:\mBbbN{}\msupplus{}. \mexists{}g:\{x:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| \mneg{}(P x)\} . (g = regularize(1;f)))
{}\mRightarrow{} (\mforall{}Q:\{x:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| \mneg{}(P x)\} {}\mrightarrow{} \mBbbB{}. \mexists{}Q':(\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}) {}\mrightarrow{} \mBbbB{}. \mforall{}x:\{x:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| \mneg{}(P x)\} . Q' x = Q x))
Date html generated:
2017_10_03-AM-10_14_31
Last ObjectModification:
2017_09_19-PM-03_51_16
Theory : reals
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