Nuprl Lemma : geo-ge-symmetry
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab ≥ cd ⇒ {ba ≥ cd ∧ ab ≥ dc ∧ ba ≥ dc})
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-ge: ab ≥ cd,
geo-point: Point,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
geo-ge: ab ≥ cd,
not: ¬A,
false: False
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab \mgeq{} cd {}\mRightarrow{} \{ba \mgeq{} cd \mwedge{} ab \mgeq{} dc \mwedge{} ba \mgeq{} dc\})
Date html generated:
2020_05_20-AM-09_53_11
Last ObjectModification:
2020_01_27-PM-11_06_53
Theory : euclidean!plane!geometry
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