Nuprl Lemma : geo-gt-prim-symmetry2
∀g:EuclideanPlane. ∀a,b,c,d:Point. (ab>cd ⇒ (ba>cd ∧ ab>dc ∧ ba>dc))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab>cd {}\mRightarrow{} (ba>cd \mwedge{} ab>dc \mwedge{} ba>dc))
Date html generated:
2020_05_20-AM-09_44_49
Last ObjectModification:
2020_01_27-PM-11_05_50
Theory : euclidean!plane!geometry
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