Nuprl Definition : real-cube-complex
RealCubeComplex(k) ==
  T:Type
  × finite(T)
  × f:T ⟶ real-cube(k)
  × (∀t1,t2:T.  ((¬(t1 = t2 ∈ T)) ⇒ (adjacent-cubes(k;f t1;f t2) ∨ f t1 # f t2)))
Definitions occuring in Statement : 
adjacent-cubes: adjacent-cubes(k;c1;c2), 
real-cube-sep: c1 # c2, 
real-cube: real-cube(k), 
finite: finite(T), 
all: ∀x:A. B[x], 
not: ¬A, 
implies: P ⇒ Q, 
or: P ∨ Q, 
apply: f a, 
function: x:A ⟶ B[x], 
product: x:A × B[x], 
universe: Type, 
equal: s = t ∈ T
Definitions occuring in definition : 
universe: Type, 
finite: finite(T), 
product: x:A × B[x], 
function: x:A ⟶ B[x], 
real-cube: real-cube(k), 
all: ∀x:A. B[x], 
implies: P ⇒ Q, 
not: ¬A, 
equal: s = t ∈ T, 
or: P ∨ Q, 
adjacent-cubes: adjacent-cubes(k;c1;c2), 
real-cube-sep: c1 # c2, 
apply: f a
FDL editor aliases : 
real-cube-complex
Latex:
RealCubeComplex(k)  ==
    T:Type
    \mtimes{}  finite(T)
    \mtimes{}  f:T  {}\mrightarrow{}  real-cube(k)
    \mtimes{}  (\mforall{}t1,t2:T.    ((\mneg{}(t1  =  t2))  {}\mRightarrow{}  (adjacent-cubes(k;f  t1;f  t2)  \mvee{}  f  t1  \#  f  t2)))
Date html generated:
2019_10_30-AM-11_31_40
Last ObjectModification:
2019_09_30-AM-11_18_03
Theory : real!vectors
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