Nuprl Lemma : det-fun_wf
∀[r:Rng]. ∀[n:ℕ]. (det-fun(r;n) ∈ Type)
Proof
Definitions occuring in Statement :
det-fun: det-fun(r;n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng: Rng
Definitions unfolded in proof :
so_apply: x[s1;s2],
not: ¬A,
false: False,
so_lambda: λ2x y.t[x; y],
infix_ap: x f y,
all: ∀x:A. B[x],
so_apply: x[s],
int_seg: {i..j-},
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
rng: Rng,
nat: ℕ,
det-fun: det-fun(r;n),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
nat_wf,
matrix-ap_wf,
rng_plus_wf,
mx_wf,
rng_times_wf,
infix_ap_wf,
matrix-mul-row_wf,
rng_minus_wf,
matrix-swap-cols_wf,
not_wf,
int_seg_wf,
all_wf,
rng_one_wf,
identity-matrix_wf,
equal_wf,
rng_car_wf,
matrix_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
int_eqEquality,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
productEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}]. (det-fun(r;n) \mmember{} Type)
Date html generated:
2018_05_21-PM-09_36_45
Last ObjectModification:
2017_12_12-AM-10_14_03
Theory : matrices
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