Nuprl Lemma : geo-isosceles_wf
∀[g1:EuclideanPlane]. ∀[a,b,c:Point]. (ISOΔ(a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-isosceles: ISOΔ(a;b;c),
euclidean-plane: EuclideanPlane,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
geo-isosceles: ISOΔ(a;b;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
geo-lsep_wf,
geo-cong-angle_wf,
geo-congruent_wf
Rules used in proof :
isect_memberEquality,
independent_isectElimination,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g1:EuclideanPlane]. \mforall{}[a,b,c:Point]. (ISO\mDelta{}(a;b;c) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_55_39
Last ObjectModification:
2017_08_06-PM-07_58_45
Theory : euclidean!plane!geometry
Home
Index