Nuprl Lemma : r2-det-syzygy
∀[p,q,r,u,v,w,x,y,z:ℝ^2].
(((|pqw| * |rpv| * |qry| * |prx| * |quz|)
+ (|rpv| * |qru| * |rpz| * |qpy| * |qwx|)
+ (|qru| * |pqw| * |rpz| * |prx| * |qvy|)
+ (|qru| * |pqw| * |rpz| * |qpy| * |rvx|)
+ (|pqw| * |rpv| * |pqx| * |rqz| * |ruy|)
+ (|rpv| * |qru| * |pqx| * |qpy| * |rwz|)
+ (|rpv| * |qru| * |pqx| * |rqz| * |pwy|)
+ (|qru| * |pqw| * |qry| * |prx| * |pvz|)
+ (|pqw| * |rpv| * |qry| * |rqz| * |pux|))
= r0)
Proof
Definitions occuring in Statement :
r2-det: |pqr|,
real-vec: ℝ^n,
req: x = y,
rmul: a * b,
radd: a + b,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
nat: ℕ,
uiff: uiff(P;Q),
top: Top,
req_int_terms: t1 ≡ t2,
has-value: (a)↓,
it: ⋅,
nil: [],
ml-term-to-poly: ml-term-to-poly(t),
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
squash: ↓T,
less_than: a < b,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
real-vec: ℝ^n,
r2-det: |pqr|,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
le_wf,
false_wf,
real-vec_wf,
r2-det_wf,
req_witness,
req-iff-rsub-is-0,
real_term_value_const_lemma,
real_term_value_var_lemma,
real_term_value_mul_lemma,
real_term_value_add_lemma,
real_term_value_sub_lemma,
evalall-sqequal,
itermConstant_wf,
itermVar_wf,
itermMultiply_wf,
itermAdd_wf,
itermSubtract_wf,
real_polynomial_null,
int-to-real_wf,
lelt_wf,
rsub_wf,
rmul_wf,
radd_wf
Rules used in proof :
independent_functionElimination,
productElimination,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
mlComputation,
sqleReflexivity,
computeAll,
independent_isectElimination,
dependent_functionElimination,
baseClosed,
hypothesisEquality,
imageMemberEquality,
hypothesis,
lambdaFormation,
sqequalRule,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
because_Cache,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[p,q,r,u,v,w,x,y,z:\mBbbR{}\^{}2].
(((|pqw| * |rpv| * |qry| * |prx| * |quz|)
+ (|rpv| * |qru| * |rpz| * |qpy| * |qwx|)
+ (|qru| * |pqw| * |rpz| * |prx| * |qvy|)
+ (|qru| * |pqw| * |rpz| * |qpy| * |rvx|)
+ (|pqw| * |rpv| * |pqx| * |rqz| * |ruy|)
+ (|rpv| * |qru| * |pqx| * |qpy| * |rwz|)
+ (|rpv| * |qru| * |pqx| * |rqz| * |pwy|)
+ (|qru| * |pqw| * |qry| * |prx| * |pvz|)
+ (|pqw| * |rpv| * |qry| * |rqz| * |pux|))
= r0)
Date html generated:
2017_10_03-AM-11_43_08
Last ObjectModification:
2017_08_11-PM-10_26_57
Theory : reals
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