Nuprl Lemma : real-cube-interior_wf
∀[n:ℕ]. ∀[a,b:ℕn ⟶ ℝ]. (real-cube-interior(n;a;b) ∈ Type)
Proof
Definitions occuring in Statement :
real-cube-interior: real-cube-interior(n;a;b),
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
real-vec: ℝ^n,
and: P ∧ Q,
nat: ℕ,
top: Top,
all: ∀x:A. B[x],
real-cube-interior: real-cube-interior(n;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
real_wf,
rless_wf,
int_seg_wf,
real-vec_wf,
istype-void,
member_rooint_lemma
Rules used in proof :
universeIsType,
functionIsType,
isectIsTypeImplies,
inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
productEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
functionEquality,
hypothesisEquality,
isectElimination,
setEquality,
hypothesis,
voidElimination,
isect_memberEquality_alt,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbN{}n {}\mrightarrow{} \mBbbR{}]. (real-cube-interior(n;a;b) \mmember{} Type)
Date html generated:
2019_11_06-PM-00_35_55
Last ObjectModification:
2019_11_05-AM-11_13_23
Theory : real!vectors
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