Nuprl Lemma : mx_wf
∀[n,m:ℤ]. ∀[r:RngSig]. ∀[M:ℕn ⟶ ℕm ⟶ |r|]. (matrix(M[x;y]) ∈ Matrix(n;m;r))
Proof
Definitions occuring in Statement :
mx: matrix(M[x; y]),
matrix: Matrix(n;m;r),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
so_apply: x[s1;s2],
mx: matrix(M[x; y]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
matrix: Matrix(n;m;r)
Lemmas referenced :
rng_sig_wf,
rng_car_wf,
int_seg_wf
Rules used in proof :
intEquality,
because_Cache,
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[r:RngSig]. \mforall{}[M:\mBbbN{}n {}\mrightarrow{} \mBbbN{}m {}\mrightarrow{} |r|]. (matrix(M[x;y]) \mmember{} Matrix(n;m;r))
Date html generated:
2018_05_21-PM-09_34_07
Last ObjectModification:
2017_12_11-PM-00_29_21
Theory : matrices
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