Nuprl Lemma : matrix-det-dim0
∀[r:Rng]. ∀[M:Top]. (|M| = 1 ∈ |r|)
Proof
Definitions occuring in Statement :
matrix-det: |M|,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
equal: s = t ∈ T,
rng: Rng,
rng_one: 1,
rng_car: |r|
Definitions unfolded in proof :
and: P ∧ Q,
rng: Rng,
let: let,
permutation-sign: permutation-sign(n;f),
so_apply: x[s],
top: Top,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
matrix-det: |M|,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
top_wf,
rng_one_wf,
rng_plus_zero,
int_prod0_lemma,
rng_lsum_nil_lemma,
rng_prod_empty_lemma,
rng_lsum_cons_lemma,
permutations-list-0
Rules used in proof :
because_Cache,
axiomEquality,
productElimination,
rename,
setElimination,
hypothesisEquality,
isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[M:Top]. (|M| = 1)
Date html generated:
2018_05_21-PM-09_35_33
Last ObjectModification:
2018_01_02-PM-01_13_19
Theory : matrices
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