Nuprl Lemma : swap-rows-is-transpose-swap-cols
∀[M,i,j:Top]. (matrix-swap-rows(M;i;j) ~ matrix-swap-cols(M';i;j)')
Proof
Definitions occuring in Statement :
matrix-swap-cols: matrix-swap-cols(M;i;j),
matrix-swap-rows: matrix-swap-rows(M;i;j),
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-swap-rows: matrix-swap-rows(M;i;j),
matrix-swap-cols: matrix-swap-cols(M;i;j),
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,i,j:Top]. (matrix-swap-rows(M;i;j) \msim{} matrix-swap-cols(M';i;j)')
Date html generated:
2018_05_21-PM-09_36_19
Last ObjectModification:
2017_12_11-PM-04_12_13
Theory : matrices
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