Nuprl Lemma : in-rat-cube_wf
∀[k:ℕ]. ∀[p:ℝ^k]. ∀[c:ℚCube(k)]. (in-rat-cube(k;p;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
in-rat-cube: in-rat-cube(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 :
pi2: snd(t),
real-vec: ℝ^n,
pi1: fst(t),
rational-interval: ℚInterval,
implies: P ⇒ Q,
rational-cube: ℚCube(k),
and: P ∧ Q,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
in-rat-cube: in-rat-cube(k;p;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
real-vec_wf,
rational-cube_wf,
rat2real_wf,
rleq_wf,
int_seg_wf
Rules used in proof :
isectIsTypeImplies,
isect_memberEquality_alt,
universeIsType,
axiomEquality,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
productElimination,
lambdaFormation_alt,
inhabitedIsType,
applyEquality,
productEquality,
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)]. (in-rat-cube(k;p;c) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-10_12_46
Last ObjectModification:
2019_10_26-AM-11_50_27
Theory : real!vectors
Home
Index