Nuprl Lemma : ip-between-sep
∀rv:InnerProductSpace. ∀a,c:Point. ∀[b:Point]. (a # c) supposing (a # b and a_b_c)
Proof
Definitions occuring in Statement :
ip-between: a_b_c,
inner-product-space: InnerProductSpace,
ss-sep: x # y,
ss-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ip-between: a_b_c,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ,
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
rge: x ≥ y
Lemmas referenced :
req_witness,
radd_wf,
rmul_wf,
rv-norm_wf,
rv-sub_wf,
inner-product-space_subtype,
rv-ip_wf,
int-to-real_wf,
sq_stable__rv-sep-ext,
ip-dist-between,
ss-sep_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
ip-between_wf,
ss-point_wf,
rv-norm-positive,
rv-sep-iff,
rv-norm-nonneg,
real_wf,
rleq_wf,
req_wf,
trivial-rless-radd,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rleq_transitivity,
radd_functionality_wrt_rleq,
rleq_weakening,
req_inversion,
rv-norm-positive-iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
natural_numberEquality,
independent_functionElimination,
rename,
dependent_functionElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
imageElimination,
instantiate,
productElimination,
independent_pairFormation,
lambdaEquality,
setElimination,
setEquality,
productEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}a,c:Point. \mforall{}[b:Point]. (a \# c) supposing (a \# b and a\_b\_c)
Date html generated:
2017_10_05-AM-00_01_50
Last ObjectModification:
2017_03_12-PM-03_14_40
Theory : inner!product!spaces
Home
Index