Nuprl Lemma : test-ring-req
∀v,v1,v2,v3,v4,v5,v6,v7,v8,v9:ℝ.
((((((v6 * v3) + (v2 * v5) + (v4 * v7)) - (v7 * v2) + (v3 * v4) + (v5 * v6))
* (((v6 * v9) + (v8 * v1) + (v * v7)) - (v7 * v8) + (v9 * v) + (v1 * v6)))
+ ((((v * v7) + (v6 * v5) + (v4 * v1)) - (v1 * v6) + (v7 * v4) + (v5 * v))
* (((v6 * v9) + (v8 * v3) + (v2 * v7)) - (v7 * v8) + (v9 * v2) + (v3 * v6)))
+ ((((v * v3) + (v2 * v7) + (v6 * v1)) - (v1 * v2) + (v3 * v6) + (v7 * v))
* (((v6 * v9) + (v8 * v5) + (v4 * v7)) - (v7 * v8) + (v9 * v4) + (v5 * v6))))
= r0)
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
rmul: a * b,
radd: a + b,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
req_int_terms: t1 ≡ t2,
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top
Lemmas referenced :
real_wf,
radd_wf,
rmul_wf,
rsub_wf,
int-to-real_wf,
itermSubtract_wf,
itermAdd_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
natural_numberEquality,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
approximateComputation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}v,v1,v2,v3,v4,v5,v6,v7,v8,v9:\mBbbR{}.
((((((v6 * v3) + (v2 * v5) + (v4 * v7)) - (v7 * v2) + (v3 * v4) + (v5 * v6))
* (((v6 * v9) + (v8 * v1) + (v * v7)) - (v7 * v8) + (v9 * v) + (v1 * v6)))
+ ((((v * v7) + (v6 * v5) + (v4 * v1)) - (v1 * v6) + (v7 * v4) + (v5 * v))
* (((v6 * v9) + (v8 * v3) + (v2 * v7)) - (v7 * v8) + (v9 * v2) + (v3 * v6)))
+ ((((v * v3) + (v2 * v7) + (v6 * v1)) - (v1 * v2) + (v3 * v6) + (v7 * v))
* (((v6 * v9) + (v8 * v5) + (v4 * v7)) - (v7 * v8) + (v9 * v4) + (v5 * v6))))
= r0)
Date html generated:
2017_10_02-PM-07_20_48
Last ObjectModification:
2017_07_28-AM-07_21_41
Theory : reals
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