Nuprl Lemma : sq_stable__real-vec-indep
∀[k:ℕ]. ∀[L:ℝ^k List]. SqStable(real-vec-indep(k;L))
Proof
Definitions occuring in Statement :
real-vec-indep: real-vec-indep(k;L),
real-vec: ℝ^n,
list: T List,
nat: ℕ,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
real-vec-indep: real-vec-indep(k;L),
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B
Lemmas referenced :
sq_stable__from_stable,
real-vec-indep_wf,
stable__real-vec-indep,
req_witness,
int-to-real_wf,
list_wf,
real-vec_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
productElimination,
functionIsTypeImplies,
inhabitedIsType,
universeIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[L:\mBbbR{}\^{}k List]. SqStable(real-vec-indep(k;L))
Date html generated:
2019_10_30-AM-08_04_53
Last ObjectModification:
2019_09_17-PM-06_04_41
Theory : reals
Home
Index