Nuprl Lemma : trans-apply_wf
∀rv:InnerProductSpace. ∀T:ℝ ⟶ Point ⟶ Point. ∀x:Point. ∀[t:ℝ]. (T_t(x) ∈ Point)
Proof
Definitions occuring in Statement :
trans-apply: T_t(x),
inner-product-space: InnerProductSpace,
real: ℝ,
ss-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
trans-apply: T_t(x),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
real_wf,
ss-point_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
functionExtensionality,
hypothesisEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination,
thin,
instantiate,
independent_isectElimination,
functionEquality,
because_Cache
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}T:\mBbbR{} {}\mrightarrow{} Point {}\mrightarrow{} Point. \mforall{}x:Point. \mforall{}[t:\mBbbR{}]. (T\_t(x) \mmember{} Point)
Date html generated:
2017_10_05-AM-00_21_17
Last ObjectModification:
2017_06_24-PM-03_58_40
Theory : inner!product!spaces
Home
Index