Nuprl Lemma : not-rv-pos-angle-implies2
∀n:ℕ. ∀a,b,c:ℝ^n.  ((¬rv-pos-angle(n;a;b;c)) 
⇒ (¬((¬rv-T(n;a;b;c)) ∧ (¬rv-T(n;b;c;a)) ∧ (¬rv-T(n;c;a;b)))))
Proof
Definitions occuring in Statement : 
rv-T: rv-T(n;a;b;c)
, 
rv-pos-angle: rv-pos-angle(n;a;b;c)
, 
real-vec: ℝ^n
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
and: P ∧ Q
, 
not: ¬A
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
false: False
, 
or: P ∨ Q
, 
cand: A c∧ B
Lemmas referenced : 
not-rv-pos-angle-implies, 
not_wf, 
rv-pos-angle_wf, 
real-vec_wf, 
nat_wf, 
false_wf, 
or_wf, 
real-vec-sep_wf, 
rv-T_wf, 
rv-T-iff, 
rv-between_wf, 
minimal-double-negation-hyp-elim, 
minimal-not-not-excluded-middle
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
independent_functionElimination, 
functionEquality, 
productEquality, 
because_Cache, 
productElimination, 
voidElimination, 
unionElimination, 
independent_pairFormation
Latex:
\mforall{}n:\mBbbN{}.  \mforall{}a,b,c:\mBbbR{}\^{}n.
    ((\mneg{}rv-pos-angle(n;a;b;c))  {}\mRightarrow{}  (\mneg{}((\mneg{}rv-T(n;a;b;c))  \mwedge{}  (\mneg{}rv-T(n;b;c;a))  \mwedge{}  (\mneg{}rv-T(n;c;a;b)))))
Date html generated:
2017_10_03-AM-11_20_11
Last ObjectModification:
2017_06_14-PM-06_12_44
Theory : reals
Home
Index