Nuprl Lemma : stable__in-rat-cube
∀[k:ℕ]. ∀[p:ℝ^k]. ∀[c:ℚCube(k)]. Stable{in-rat-cube(k;p;c)}
Proof
Definitions occuring in Statement :
in-rat-cube: in-rat-cube(k;p;c),
real-vec: ℝ^n,
nat: ℕ,
stable: Stable{P},
uall: ∀[x:A]. B[x],
rational-cube: ℚCube(k)
Definitions unfolded in proof :
le: A ≤ B,
rnonneg: rnonneg(x),
rleq: x ≤ y,
uimplies: b supposing a,
stable: Stable{P},
so_apply: x[s],
pi2: snd(t),
real-vec: ℝ^n,
pi1: fst(t),
rational-interval: ℚInterval,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rational-cube: ℚCube(k),
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
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,
le_witness_for_triv,
stable__rleq,
stable__and,
rat2real_wf,
rleq_wf,
int_seg_wf,
stable__all
Rules used in proof :
isectIsTypeImplies,
functionIsTypeImplies,
independent_isectElimination,
independent_pairEquality,
isect_memberEquality_alt,
universeIsType,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
productElimination,
lambdaFormation_alt,
inhabitedIsType,
applyEquality,
productEquality,
lambdaEquality_alt,
sqequalRule,
hypothesis,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}k]. \mforall{}[c:\mBbbQ{}Cube(k)]. Stable\{in-rat-cube(k;p;c)\}
Date html generated:
2019_11_04-PM-04_43_16
Last ObjectModification:
2019_10_31-PM-04_14_52
Theory : real!vectors
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