Nuprl Lemma : matrix-transpose-twice
∀[n,m:ℤ]. ∀[r:RngSig]. ∀[M:Matrix(n;m;r)]. (M'' = M ∈ Matrix(n;m;r))
Proof
Definitions occuring in Statement :
matrix-transpose: M',
matrix: Matrix(n;m;r),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
mx: matrix(M[x; y]),
matrix-ap: M[i,j],
matrix-transpose: M',
matrix: Matrix(n;m;r),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
matrix_wf,
int_seg_wf,
matrix-ap_wf
Rules used in proof :
intEquality,
because_Cache,
axiomEquality,
isect_memberEquality,
natural_numberEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
functionExtensionality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[r:RngSig]. \mforall{}[M:Matrix(n;m;r)]. (M'' = M)
Date html generated:
2018_05_21-PM-09_34_15
Last ObjectModification:
2017_12_13-PM-03_10_34
Theory : matrices
Home
Index