Nuprl Lemma : transpose-matrix-minor
∀[i,j,M:Top]. (matrix-minor(i;j;M)' ~ matrix-minor(j;i;M'))
Proof
Definitions occuring in Statement :
matrix-minor: matrix-minor(i;j;m),
matrix-transpose: M',
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
mx: matrix(M[x; y]),
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
top: Top,
all: ∀x:A. B[x],
matrix-minor: matrix-minor(i;j;m),
matrix-transpose: M',
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
matrix_ap_mx_lemma
Rules used in proof :
because_Cache,
hypothesisEquality,
isectElimination,
sqequalAxiom,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[i,j,M:Top]. (matrix-minor(i;j;M)' \msim{} matrix-minor(j;i;M'))
Date html generated:
2018_05_21-PM-09_37_22
Last ObjectModification:
2017_12_14-PM-00_26_06
Theory : matrices
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