Nuprl Lemma : in-cube-complex_wf
∀[k:ℕ]. ∀[p:ℝ^k]. ∀[cc:RealCubeComplex(k)]. (in-cube-complex(k;p;cc) ∈ ℙ)
Proof
Definitions occuring in Statement :
in-cube-complex: in-cube-complex(k;p;cc),
real-cube-complex: RealCubeComplex(k),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
in-cube-complex: in-cube-complex(k;p;cc),
spreadn: spread4,
real-cube-complex: RealCubeComplex(k),
prop: ℙ,
exists: ∃x:A. B[x]
Lemmas referenced :
in-real-cube_wf,
real-cube-complex_wf,
real-vec_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
productEquality,
hypothesisEquality,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}k]. \mforall{}[cc:RealCubeComplex(k)]. (in-cube-complex(k;p;cc) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_31_49
Last ObjectModification:
2019_09_30-AM-11_22_44
Theory : real!vectors
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