Nuprl Lemma : rv-pos-angle-implies-separated2
∀n:ℕ. ∀a,b,c:ℝ^n. (rv-pos-angle(n;a;b;c) ⇒ a ≠ b)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
rv-pos-angle: rv-pos-angle(n;a;b;c),
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
rv-pos-angle-permute,
rv-pos-angle-implies-separated,
rv-pos-angle_wf,
real-vec_wf,
nat_wf,
real-vec-sep-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
because_Cache,
isectElimination,
productElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c:\mBbbR{}\^{}n. (rv-pos-angle(n;a;b;c) {}\mRightarrow{} a \mneq{} b)
Date html generated:
2017_10_03-AM-11_04_46
Last ObjectModification:
2017_03_02-PM-05_11_32
Theory : reals
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