Nuprl Lemma : scalar-triple-product_wf
∀[r:Rng]. ∀[a,b,c:ℕ3 ⟶ |r|]. (|a,b,c| ∈ |r|)
Proof
Definitions occuring in Statement :
scalar-triple-product: |a,b,c|,
int_seg: {i..j-},
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 :
rng: Rng,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
scalar-triple-product: |a,b,c|,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
rng_car_wf,
cross-product_wf,
int_seg_wf,
le_wf,
false_wf,
scalar-product_wf
Rules used in proof :
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
rename,
setElimination,
applyEquality,
functionExtensionality,
hypothesis,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[a,b,c:\mBbbN{}3 {}\mrightarrow{} |r|]. (|a,b,c| \mmember{} |r|)
Date html generated:
2018_05_21-PM-09_42_17
Last ObjectModification:
2017_12_18-PM-00_47_36
Theory : matrices
Home
Index