Nuprl Lemma : in-hull_wf
∀[g:OrientedPlane]. ∀[xs:{xs:Point List| geo-general-position(g;xs)} ]. ∀[i,j:ℕ||xs||].
ij ∈ Hull(xs) ∈ ℙ supposing ¬(i = j ∈ ℤ)
Proof
Definitions occuring in Statement :
in-hull: ij ∈ Hull(xs),
geo-general-position: geo-general-position(g;xs),
oriented-plane: OrientedPlane,
geo-point: Point,
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
top: Top,
all: ∀x:A. B[x],
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
lelt: i ≤ j < k,
not: ¬A,
cand: A c∧ B,
and: P ∧ Q,
int_seg: {i..j-},
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
guard: {T},
subtype_rel: A ⊆r B,
in-hull: ij ∈ Hull(xs),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-general-position_wf,
list_wf,
set_wf,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
full-omega-unsat,
int_seg_properties,
left-test_wf,
assert_wf,
equal_wf,
not_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
Error :oriented-plane_wf,
subtype_rel_transitivity,
Error :oriented-plane-subtype,
basic-geometry--subtype,
geo-point_wf,
length_wf,
int_seg_wf,
all_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
productElimination,
lambdaFormation,
dependent_set_memberEquality,
because_Cache,
intEquality,
functionEquality,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
natural_numberEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
rename,
thin,
setElimination,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:OrientedPlane]. \mforall{}[xs:\{xs:Point List| geo-general-position(g;xs)\} ]. \mforall{}[i,j:\mBbbN{}||xs||].
ij \mmember{} Hull(xs) \mmember{} \mBbbP{} supposing \mneg{}(i = j)
Date html generated:
2017_10_02-PM-06_51_41
Last ObjectModification:
2017_08_08-PM-00_39_02
Theory : euclidean!plane!geometry
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