Nuprl Lemma : scalar-product_wf
∀[r:Rng]. ∀[n:ℕ]. ∀[a,b:ℕn ⟶ |r|]. ((a . b) ∈ |r|)
Proof
Definitions occuring in Statement :
scalar-product: (a . b),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
so_apply: x[s],
rng: Rng,
infix_ap: x f y,
so_lambda: λ2x.t[x],
nat: ℕ,
scalar-product: (a . b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
nat_wf,
rng_car_wf,
int_seg_wf,
rng_times_wf,
rng_sum_wf
Rules used in proof :
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
hypothesis,
because_Cache,
rename,
setElimination,
natural_numberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbN{}n {}\mrightarrow{} |r|]. ((a . b) \mmember{} |r|)
Date html generated:
2018_05_21-PM-09_41_54
Last ObjectModification:
2017_12_18-PM-00_44_17
Theory : matrices
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