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
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