Nuprl Lemma : rv-pos-angle-symmetry
∀n:ℕ. ∀a,b,c:ℝ^n. (rv-pos-angle(n;a;b;c) ⇒ rv-pos-angle(n;c;b;a))
Proof
Definitions occuring in Statement :
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,
rv-pos-angle: rv-pos-angle(n;a;b;c),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rv-pos-angle_wf,
real-vec_wf,
nat_wf,
rmul_comm,
real-vec-norm_wf,
real-vec-sub_wf,
rabs_wf,
dot-product_wf,
rmul_wf,
rless_functionality,
req_weakening,
rabs_functionality,
dot-product-comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c:\mBbbR{}\^{}n. (rv-pos-angle(n;a;b;c) {}\mRightarrow{} rv-pos-angle(n;c;b;a))
Date html generated:
2017_10_03-AM-10_56_53
Last ObjectModification:
2017_03_01-PM-05_19_30
Theory : reals
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