Nuprl Definition : adjacent-cubes
adjacent-cubes(k;c1;c2) ==
∃i:ℕk
((∀j:ℕk. ((¬(j = i ∈ ℤ)) ⇒ (((c1- j) = (c2- j)) ∧ ((c1+ j) = (c2+ j)))))
∧ (((c1- i) = (c2+ i)) ∨ ((c2- i) = (c1+ i))))
Definitions occuring in Statement :
cube-lower: c-,
cube-upper: c+,
req: x = y,
int_seg: {i..j-},
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions occuring in definition :
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
int_seg: {i..j-},
natural_number: $n,
implies: P ⇒ Q,
not: ¬A,
equal: s = t ∈ T,
int: ℤ,
and: P ∧ Q,
or: P ∨ Q,
req: x = y,
cube-lower: c-,
apply: f a,
cube-upper: c+
FDL editor aliases :
adjacent-cubes
Latex:
adjacent-cubes(k;c1;c2) ==
\mexists{}i:\mBbbN{}k
((\mforall{}j:\mBbbN{}k. ((\mneg{}(j = i)) {}\mRightarrow{} (((c1- j) = (c2- j)) \mwedge{} ((c1+ j) = (c2+ j)))))
\mwedge{} (((c1- i) = (c2+ i)) \mvee{} ((c2- i) = (c1+ i))))
Date html generated:
2019_10_30-AM-11_31_32
Last ObjectModification:
2019_09_27-PM-01_34_09
Theory : real!vectors
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