Nuprl Lemma : adj-solution_wf
∀[r:CRng]. ∀[n,m:ℕ]. ∀[A:Matrix(n;n;r)]. ∀[c:|r|]. ∀[b:Matrix(n;m;r)]. (adj-solution(r;n;A;c;b) ∈ Matrix(n;m;r))
Proof
Definitions occuring in Statement :
adj-solution: adj-solution(r;n;A;c;b),
matrix: Matrix(n;m;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng,
rng_car: |r|
Definitions unfolded in proof :
nat: ℕ,
rng: Rng,
crng: CRng,
adj-solution: adj-solution(r;n;A;c;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
crng_wf,
nat_wf,
rng_car_wf,
matrix_wf,
adjugate_wf,
matrix-times_wf,
matrix-scalar-mul_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:CRng]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[A:Matrix(n;n;r)]. \mforall{}[c:|r|]. \mforall{}[b:Matrix(n;m;r)].
(adj-solution(r;n;A;c;b) \mmember{} Matrix(n;m;r))
Date html generated:
2018_05_21-PM-09_40_12
Last ObjectModification:
2017_12_14-PM-03_27_26
Theory : matrices
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