Nuprl Lemma : matrix-det_wf
∀[r:Rng]. ∀[n:ℕ]. ∀[M:Matrix(n;n;r)]. (|M| ∈ |r|)
Proof
Definitions occuring in Statement :
matrix-det: |M|,
matrix: Matrix(n;m;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
all: ∀x:A. B[x],
prop: ℙ,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
so_apply: x[s],
rng: Rng,
subtype_rel: A ⊆r B,
injection: A →⟶ B,
so_lambda: λ2x.t[x],
nat: ℕ,
let: let,
matrix-det: |M|,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
nat_wf,
matrix_wf,
l_member_wf,
all_wf,
no_repeats_wf,
list_wf,
permutations-list_wf,
rng_minus_wf,
matrix-ap_wf,
rng_prod_wf,
permutation-sign_wf,
int_seg_wf,
injection_wf,
rng_lsum_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
setEquality,
applyEquality,
int_eqEquality,
lambdaEquality,
hypothesis,
because_Cache,
rename,
setElimination,
natural_numberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}]. \mforall{}[M:Matrix(n;n;r)]. (|M| \mmember{} |r|)
Date html generated:
2018_05_21-PM-09_35_31
Last ObjectModification:
2017_12_11-PM-00_57_16
Theory : matrices
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