Nuprl Lemma : matrix-times_wf
∀[n,k,m:ℤ]. ∀[r:Rng]. ∀[M:Matrix(n;k;r)]. ∀[N:Matrix(k;m;r)]. ((M*N) ∈ Matrix(n;m;r))
Proof
Definitions occuring in Statement :
matrix-times: (M*N),
matrix: Matrix(n;m;r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
rng: Rng
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_apply: x[s],
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
rng: Rng,
matrix-times: (M*N),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
matrix_wf,
int_seg_wf,
matrix-ap_wf,
rng_times_wf,
rng_sum_wf,
mx_wf
Rules used in proof :
intEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
natural_numberEquality,
lambdaEquality,
hypothesis,
because_Cache,
rename,
setElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n,k,m:\mBbbZ{}]. \mforall{}[r:Rng]. \mforall{}[M:Matrix(n;k;r)]. \mforall{}[N:Matrix(k;m;r)]. ((M*N) \mmember{} Matrix(n;m;r))
Date html generated:
2018_05_21-PM-09_34_37
Last ObjectModification:
2017_12_11-PM-00_29_28
Theory : matrices
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