Nuprl Lemma : hyptrans_wf
∀[rv:InnerProductSpace]. ∀[e,x:Point]. ∀[t:ℝ]. (hyptrans(rv;e;t;x) ∈ Point)
Proof
Definitions occuring in Statement :
hyptrans: hyptrans(rv;e;t;x),
inner-product-space: InnerProductSpace,
real: ℝ,
ss-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hyptrans: hyptrans(rv;e;t;x),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
rv-add_wf,
inner-product-space_subtype,
rv-mul_wf,
radd_wf,
rmul_wf,
rv-ip_wf,
rsub_wf,
cosh_wf,
int-to-real_wf,
rsqrt_wf,
radd-non-neg,
rleq-int,
false_wf,
rv-ip-nonneg,
rleq_wf,
sinh_wf,
real_wf,
ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairFormation,
lambdaFormation,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[e,x:Point]. \mforall{}[t:\mBbbR{}]. (hyptrans(rv;e;t;x) \mmember{} Point)
Date html generated:
2017_10_05-AM-00_27_13
Last ObjectModification:
2017_06_21-AM-11_33_45
Theory : inner!product!spaces
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