Nuprl Lemma : geo-tar-opp-side_wf
∀[e:BasicGeometry]. ∀[A,B,P,Q:Point]. (geo-tar-opp-side(e;A;B;P;Q) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-tar-opp-side: geo-tar-opp-side(e;a;b;p;q),
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
exists: ∃x:A. B[x],
so_apply: x[s],
basic-geometry: BasicGeometry,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
geo-tar-opp-side: geo-tar-opp-side(e;a;b;p;q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-between_wf,
geo-colinear_wf,
geo-point_wf,
exists_wf,
geo-sep-line_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
lambdaEquality,
because_Cache,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[A,B,P,Q:Point]. (geo-tar-opp-side(e;A;B;P;Q) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_23_09
Last ObjectModification:
2017_08_05-PM-04_17_21
Theory : euclidean!plane!geometry
Home
Index