Nuprl Lemma : rat-cube-third_wf
∀[k:ℕ]. ∀[p:ℝ^k]. ∀[c:ℚCube(k)]. (rat-cube-third(k;p;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
rat-cube-third: rat-cube-third(k;p;c),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
rational-cube: ℚCube(k)
Definitions unfolded in proof :
rational-cube: ℚCube(k),
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
rat-cube-third: rat-cube-third(k;p;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
real-vec_wf,
rational-cube_wf,
rat-interval-third_wf,
int_seg_wf
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}k]. \mforall{}[c:\mBbbQ{}Cube(k)]. (rat-cube-third(k;p;c) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_03_45
Last ObjectModification:
2019_10_30-PM-01_32_06
Theory : real!vectors
Home
Index