Nuprl Lemma : stable_real-vec-be
∀n:ℕ. ∀a,c:ℝ^n. (a ≠ c ⇒ (∀b:ℝ^n. Stable{real-vec-be(n;a;b;c)}))
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
real-vec-be: real-vec-be(n;a;b;c),
real-vec: ℝ^n,
nat: ℕ,
stable: Stable{P},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
real-vec-be: real-vec-be(n;a;b;c),
stable: Stable{P},
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
real-vec: ℝ^n,
cand: A c∧ B,
top: Top,
req-vec: req-vec(n;x;y),
real-vec-mul: a*X,
real-vec-add: X + Y,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rsub: x - y
Lemmas referenced :
not_wf,
exists_wf,
real_wf,
i-member_wf,
rccint_wf,
int-to-real_wf,
req-vec_wf,
real-vec-add_wf,
real-vec-mul_wf,
rsub_wf,
real-vec_wf,
real-vec-sep_wf,
nat_wf,
real-vec-sep-implies,
rabs-positive-iff,
rdiv_wf,
member_rccint_lemma,
stable__and,
rleq_wf,
stable__rleq,
rmul_preserves_req,
req_wf,
rmul_wf,
radd_wf,
rminus_wf,
req_weakening,
uiff_transitivity,
req_functionality,
rmul-rdiv-cancel2,
req_transitivity,
rmul-distrib,
radd_functionality,
rmul_over_rminus,
rminus_functionality,
rmul_comm,
rmul-one-both,
req_inversion,
radd-assoc,
radd-ac,
radd_comm,
radd-rminus-assoc,
i-member_functionality,
stable__req-vec,
req-vec_functionality,
req-vec_weakening,
real-vec-add_functionality,
real-vec-mul_functionality,
rsub_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
hypothesis,
productEquality,
natural_numberEquality,
rename,
independent_functionElimination,
productElimination,
because_Cache,
dependent_pairFormation,
applyEquality,
independent_isectElimination,
independent_pairFormation,
isect_memberEquality,
voidEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,c:\mBbbR{}\^{}n. (a \mneq{} c {}\mRightarrow{} (\mforall{}b:\mBbbR{}\^{}n. Stable\{real-vec-be(n;a;b;c)\}))
Date html generated:
2016_10_26-AM-10_44_41
Last ObjectModification:
2016_09_26-PM-01_51_08
Theory : reals
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