Nuprl Lemma : another-r2-det-identity
∀[p,q,r,t,s:ℝ^2]. (((|tqr| * |tsp|) + (|ptr| * |tsq|) + (|pqt| * |tsr|)) = 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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
r2-det: |pqr|,
all: ∀x:A. B[x],
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
nat: ℕ
Lemmas referenced :
test-ring-req,
false_wf,
lelt_wf,
req_witness,
radd_wf,
rmul_wf,
r2-det_wf,
int-to-real_wf,
real-vec_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
applyEquality,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
imageMemberEquality,
hypothesisEquality,
baseClosed,
isectElimination,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[p,q,r,t,s:\mBbbR{}\^{}2]. (((|tqr| * |tsp|) + (|ptr| * |tsq|) + (|pqt| * |tsr|)) = r0)
Date html generated:
2017_10_03-AM-11_42_49
Last ObjectModification:
2017_06_09-PM-01_56_16
Theory : reals
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