Nuprl Lemma : geo-equilateral_wf
∀[g1:EuclideanPlaneStructure]. ∀[a,b,c:Point]. (EQΔ(a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-equilateral: EQΔ(a;b;c),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
geo-equilateral: EQΔ(a;b;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
geo-point_wf,
geo-lsep_wf,
euclidean-plane-structure-subtype,
geo-congruent_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g1:EuclideanPlaneStructure]. \mforall{}[a,b,c:Point]. (EQ\mDelta{}(a;b;c) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-04_41_50
Last ObjectModification:
2017_08_05-AM-08_26_36
Theory : euclidean!plane!geometry
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