Nuprl Lemma : rv-pos-angle-not-between
∀[n:ℕ]. ∀[a,b,c:ℝ^n]. ¬a-b-c supposing rv-pos-angle(n;a;b;c)
Proof
Definitions occuring in Statement :
rv-between: 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,
rv-pos-angle: rv-pos-angle(n;a;b;c),
rv-between: a-b-c,
and: P ∧ Q,
real-vec-between: a-b-c,
exists: ∃x:A. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
req-vec: req-vec(n;x;y),
real-vec-sub: X - Y,
real-vec-mul: a*X,
real-vec-add: X + Y,
nat: ℕ,
real-vec: ℝ^n,
rsub: x - y,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
le: A ≤ B,
less_than': less_than'(a;b),
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
rv-between_wf,
rv-pos-angle_wf,
real-vec_wf,
nat_wf,
rabs_wf,
dot-product_wf,
real-vec-sub_wf,
real-vec-add_wf,
real-vec-mul_wf,
rsub_wf,
int-to-real_wf,
rmul_wf,
real-vec-norm_wf,
rless_functionality,
rabs_functionality,
dot-product_functionality,
real-vec-sub_functionality,
req-vec_weakening,
rmul_functionality,
real-vec-norm_functionality,
int_seg_wf,
req_wf,
radd_wf,
rminus_wf,
req_weakening,
uiff_transitivity,
req_functionality,
radd_functionality,
rminus_functionality,
req_transitivity,
rmul-distrib,
rmul_over_rminus,
rmul-one-both,
rmul_comm,
rminus-radd,
radd_comm,
rminus-as-rmul,
req_inversion,
radd-assoc,
radd-ac,
rmul-identity1,
rmul-distrib2,
radd-int,
rmul-zero-both,
rminus-rminus,
radd-zero-both,
equal_wf,
rnexp_wf,
false_wf,
le_wf,
rless_wf,
not_wf,
dot-product-linearity2,
real-vec-norm-mul,
rabs-rmul,
real-vec-norm-squared,
real_wf,
rnexp2-nonneg,
rabs-of-nonneg,
rnexp2,
nat_plus_properties,
nat_properties,
satisfiable-full-omega-tt,
intformless_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
rmul-ac,
rmul-assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
setElimination,
rename,
applyEquality,
minusEquality,
addEquality,
dependent_set_memberEquality,
independent_pairFormation,
addLevel,
impliesFunctionality,
imageElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidEquality,
computeAll,
levelHypothesis,
impliesLevelFunctionality
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_05_37
Last ObjectModification:
2017_03_02-PM-02_43_12
Theory : reals
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