Nuprl Lemma : matrix-scalar-mul_wf
∀[r:RngSig]. ∀[k:|r|]. ∀[n,m:ℕ]. ∀[M:Matrix(n;m;r)]. (k*M ∈ Matrix(n;m;r))
Proof
Definitions occuring in Statement :
matrix-scalar-mul: k*M,
matrix: Matrix(n;m;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
so_apply: x[s1;s2],
infix_ap: x f y,
so_lambda: λ2x y.t[x; y],
nat: ℕ,
matrix-scalar-mul: k*M,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
rng_car_wf,
nat_wf,
matrix_wf,
int_seg_wf,
matrix-ap_wf,
rng_times_wf,
mx_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:RngSig]. \mforall{}[k:|r|]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[M:Matrix(n;m;r)]. (k*M \mmember{} Matrix(n;m;r))
Date html generated:
2018_05_21-PM-09_38_23
Last ObjectModification:
2017_12_13-PM-11_18_45
Theory : matrices
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