Nuprl Lemma : sub-cube_wf
∀[k:ℕ]. ∀[up:ℕk ⟶ 𝔹]. ∀[c:real-cube(k)]. (sub-cube(up;c) ∈ real-cube(k))
Proof
Definitions occuring in Statement :
sub-cube: sub-cube(up;c),
real-cube: real-cube(k),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sub-cube: sub-cube(up;c),
real-cube: real-cube(k),
real-vec: ℝ^n,
nat: ℕ,
subtype_rel: A ⊆r B
Lemmas referenced :
ifthenelse_wf,
real_wf,
ravg_wf,
int_seg_wf,
subtype_rel_self,
real-vec_wf,
real-cube_wf,
bool_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality_alt,
extract_by_obid,
isectElimination,
applyEquality,
hypothesisEquality,
hypothesis,
because_Cache,
universeIsType,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
functionIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[up:\mBbbN{}k {}\mrightarrow{} \mBbbB{}]. \mforall{}[c:real-cube(k)]. (sub-cube(up;c) \mmember{} real-cube(k))
Date html generated:
2019_10_30-AM-11_32_08
Last ObjectModification:
2019_09_27-PM-01_56_41
Theory : real!vectors
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