Nuprl Definition : disjoint_sublists
disjoint_sublists(T;L1;L2;L) ==
∃f1:ℕ||L1|| ⟶ ℕ||L||
∃f2:ℕ||L2|| ⟶ ℕ||L||
((increasing(f1;||L1||) ∧ (∀j:ℕ||L1||. (L1[j] = L[f1 j] ∈ T)))
∧ (increasing(f2;||L2||) ∧ (∀j:ℕ||L2||. (L2[j] = L[f2 j] ∈ T)))
∧ (∀j1:ℕ||L1||. ∀j2:ℕ||L2||. (¬((f1 j1) = (f2 j2) ∈ 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,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions occuring in definition :
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
and: P ∧ Q,
increasing: increasing(f;k),
select: L[n],
all: ∀x:A. B[x],
int_seg: {i..j-},
natural_number: $n,
length: ||as||,
not: ¬A,
equal: s = t ∈ T,
int: ℤ,
apply: f a
FDL editor aliases :
disjoint_sublists
Latex:
disjoint\_sublists(T;L1;L2;L) ==
\mexists{}f1:\mBbbN{}||L1|| {}\mrightarrow{} \mBbbN{}||L||
\mexists{}f2:\mBbbN{}||L2|| {}\mrightarrow{} \mBbbN{}||L||
((increasing(f1;||L1||) \mwedge{} (\mforall{}j:\mBbbN{}||L1||. (L1[j] = L[f1 j])))
\mwedge{} (increasing(f2;||L2||) \mwedge{} (\mforall{}j:\mBbbN{}||L2||. (L2[j] = L[f2 j])))
\mwedge{} (\mforall{}j1:\mBbbN{}||L1||. \mforall{}j2:\mBbbN{}||L2||. (\mneg{}((f1 j1) = (f2 j2)))))
Date html generated:
2016_05_15-PM-01_57_42
Last ObjectModification:
2015_09_23-AM-07_37_34
Theory : list!
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