Nuprl Lemma : real-vec-norm-0
∀[n:ℕ]. (||λi.r0|| = r0)
Proof
Definitions occuring in Statement :
real-vec-norm: ||x||,
req: x = y,
int-to-real: r(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
nat: ℕ,
uimplies: b supposing a
Lemmas referenced :
req_witness,
int-to-real_wf,
istype-nat,
iff_weakening_uiff,
req_wf,
real-vec-norm_wf,
req-vec_wf,
real-vec-norm-is-0,
int_seg_wf,
req-vec_weakening
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
closedConclusion,
natural_numberEquality,
hypothesis,
because_Cache,
independent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
productElimination,
setElimination,
rename,
universeIsType,
independent_isectElimination
Latex:
\mforall{}[n:\mBbbN{}]. (||\mlambda{}i.r0|| = r0)
Date html generated:
2019_10_30-AM-08_08_00
Last ObjectModification:
2019_06_24-PM-04_36_09
Theory : reals
Home
Index