Nuprl Lemma : geo-general-position_wf
∀[g:OrientedPlane]. ∀[xs:Point List]. (geo-general-position(g;xs) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-general-position: geo-general-position(g;xs),
oriented-plane: OrientedPlane,
geo-point: Point,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
squash: ↓T,
less_than: a < b,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
and: P ∧ Q,
lelt: i ≤ j < k,
oriented-plane: Error :oriented-plane,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
geo-general-position: geo-general-position(g;xs),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
int_seg_properties,
select_wf,
geo-lsep_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,
imageElimination,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
unionElimination,
dependent_functionElimination,
productElimination,
rename,
setElimination,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:OrientedPlane]. \mforall{}[xs:Point List]. (geo-general-position(g;xs) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_50_35
Last ObjectModification:
2017_08_06-PM-07_30_32
Theory : euclidean!plane!geometry
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