Nuprl Lemma : matrix-ap_wf
∀[n,m:ℤ]. ∀[r:RngSig]. ∀[i:ℕn]. ∀[j:ℕm]. ∀[M:Matrix(n;m;r)]. (M[i,j] ∈ |r|)
Proof
Definitions occuring in Statement :
matrix-ap: M[i,j],
matrix: Matrix(n;m;r),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
matrix-ap: M[i,j],
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,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[r:RngSig]. \mforall{}[i:\mBbbN{}n]. \mforall{}[j:\mBbbN{}m]. \mforall{}[M:Matrix(n;m;r)]. (M[i,j] \mmember{} |r|)
Date html generated:
2018_05_21-PM-09_34_03
Last ObjectModification:
2017_12_11-PM-00_29_19
Theory : matrices
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