Nuprl Lemma : req-cube_wf
∀[k,k:ℕ]. ∀[c1,c2:real-cube(k)]. (req-cube(k;c1;c2) ∈ ℙ)
Proof
Definitions occuring in Statement :
req-cube: req-cube(k;c1;c2),
real-cube: real-cube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
req-cube: req-cube(k;c1;c2),
prop: ℙ,
and: P ∧ Q,
real-cube: real-cube(k),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
req-vec_wf,
real-cube_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[k,k:\mBbbN{}]. \mforall{}[c1,c2:real-cube(k)]. (req-cube(k;c1;c2) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_31_04
Last ObjectModification:
2019_09_27-PM-01_23_41
Theory : real!vectors
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