Nuprl Lemma : invertible-matrix_wf
∀[r:Rng]. ∀[n:ℕ]. ∀[A:Matrix(n;n;r)]. (invertible-matrix(r;n;A) ∈ ℙ)
Proof
Definitions occuring in Statement :
invertible-matrix: invertible-matrix(r;n;A),
matrix: Matrix(n;m;r),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
rng: Rng
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
rng: Rng,
nat: ℕ,
invertible-matrix: invertible-matrix(r;n;A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
nat_wf,
identity-matrix_wf,
matrix-times_wf,
equal_wf,
matrix_wf,
exists_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:Matrix(n;n;r)]. (invertible-matrix(r;n;A) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-09_39_55
Last ObjectModification:
2017_12_14-PM-01_19_19
Theory : matrices
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