Nuprl Definition : interleaved_family_occurence
interleaved_family_occurence(T;I;L;L2;f) ==
((∀i:I. (increasing(f i;||L i||) ∧ (∀j:ℕ||L i||. (L i[j] = L2[f i j] ∈ T))))
∧ (∀i1,i2:I. ((¬(i1 = i2 ∈ I)) ⇒ (∀j1:ℕ||L i1||. ∀j2:ℕ||L i2||. (¬((f i1 j1) = (f i2 j2) ∈ ℤ))))))
∧ (∀x:ℕ||L2||. ∃i:I. ∃j:ℕ||L i||. (x = (f i j) ∈ ℤ))
Definitions occuring in Statement :
select: L[n],
length: ||as||,
increasing: increasing(f;k),
int_seg: {i..j-},
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions occuring in definition :
and: P ∧ Q,
increasing: increasing(f;k),
select: L[n],
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
int_seg: {i..j-},
natural_number: $n,
length: ||as||,
equal: s = t ∈ T,
int: ℤ,
apply: f a
FDL editor aliases :
interleaved_family_occurence
Latex:
interleaved\_family\_occurence(T;I;L;L2;f) ==
((\mforall{}i:I. (increasing(f i;||L i||) \mwedge{} (\mforall{}j:\mBbbN{}||L i||. (L i[j] = L2[f i j]))))
\mwedge{} (\mforall{}i1,i2:I. ((\mneg{}(i1 = i2)) {}\mRightarrow{} (\mforall{}j1:\mBbbN{}||L i1||. \mforall{}j2:\mBbbN{}||L i2||. (\mneg{}((f i1 j1) = (f i2 j2)))))))
\mwedge{} (\mforall{}x:\mBbbN{}||L2||. \mexists{}i:I. \mexists{}j:\mBbbN{}||L i||. (x = (f i j)))
Date html generated:
2016_05_15-PM-02_03_56
Last ObjectModification:
2015_09_23-AM-07_37_41
Theory : list!
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