Nuprl Lemma : mul-row-is-transpose-mul-col
∀[M,r,i,k:Top]. (matrix-mul-row(r;k;i;M) ~ matrix-mul-col(r;k;i;M')')
Proof
Definitions occuring in Statement :
matrix-mul-row: matrix-mul-row(r;k;i;M),
matrix-mul-col: matrix-mul-col(r;k;i;M),
matrix-transpose: M',
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
mx: matrix(M[x; y]),
matrix-ap: M[i,j],
matrix-mul-row: matrix-mul-row(r;k;i;M),
matrix-mul-col: matrix-mul-col(r;k;i;M),
matrix-transpose: M',
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
extract_by_obid,
sqequalAxiom,
hypothesis,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[M,r,i,k:Top]. (matrix-mul-row(r;k;i;M) \msim{} matrix-mul-col(r;k;i;M')')
Date html generated:
2018_05_21-PM-09_36_22
Last ObjectModification:
2017_12_11-PM-04_25_12
Theory : matrices
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