Nuprl Lemma : in-real-cube_wf
∀[k:ℕ]. ∀[p:ℝ^k]. ∀[c:real-cube(k)]. (p ∈ c ∈ ℙ)
Proof
Definitions occuring in Statement :
in-real-cube: p ∈ c,
real-cube: real-cube(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-real-cube: p ∈ c,
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T
Lemmas referenced :
int_seg_wf,
rleq_wf,
cube-lower_wf,
subtype_rel_self,
real_wf,
cube-upper_wf,
real-cube_wf,
real-vec_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productEquality,
applyEquality,
productElimination,
imageElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}k]. \mforall{}[c:real-cube(k)]. (p \mmember{} c \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_31_20
Last ObjectModification:
2019_09_27-PM-01_27_01
Theory : real!vectors
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