Nuprl Lemma : rcolumn_wf
∀[n:ℕ]. ∀[b:ℝ^n]. (col(b) ∈ ℝ(n × 1))
Proof
Definitions occuring in Statement :
rcolumn: col(b),
rmatrix: ℝ(a × b),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
rmatrix: ℝ(a × b),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rcolumn: col(b),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat: ℕ
Lemmas referenced :
int_seg_wf,
real_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
applyEquality,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
productElimination,
hypothesis,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[b:\mBbbR{}\^{}n]. (col(b) \mmember{} \mBbbR{}(n \mtimes{} 1))
Date html generated:
2019_10_30-AM-08_11_55
Last ObjectModification:
2019_09_19-PM-00_12_49
Theory : reals
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