Nuprl Lemma : rv-pos-angle-not-be
∀[n:ℕ]. ∀[a,b,c:ℝ^n]. ¬a_b_c supposing rv-pos-angle(n;a;b;c)
Proof
Definitions occuring in Statement :
rv-be: a_b_c,
rv-pos-angle: rv-pos-angle(n;a;b;c),
real-vec: ℝ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
prop: ℙ,
rv-be: a_b_c,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
rv-pos-angle-not-between,
rv-pos-angle-implies-separated2,
rv-pos-angle-permute,
rv-be_wf,
rv-pos-angle_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b,c:\mBbbR{}\^{}n]. \mneg{}a\_b\_c supposing rv-pos-angle(n;a;b;c)
Date html generated:
2017_10_03-AM-11_32_45
Last ObjectModification:
2017_08_11-PM-10_57_04
Theory : reals
Home
Index