Nuprl Lemma : geo-gt-prim-symmetry
∀g:GeometryPrimitives. (BasicGeometryAxioms(g) ⇒ (∀a,b,c,d:Point. (ab>cd ⇒ (ba>cd ∧ ab>dc ∧ ba>dc))))
Proof
Definitions occuring in Statement :
basic-geo-axioms: BasicGeometryAxioms(g),
geo-gt-prim: ab>cd,
geo-primitives: GeometryPrimitives,
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,
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
false: False,
geo-ge: ab ≥ cd,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
cand: A c∧ B,
guard: {T}
Latex:
\mforall{}g:GeometryPrimitives
(BasicGeometryAxioms(g) {}\mRightarrow{} (\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_42_17
Last ObjectModification:
2020_01_27-PM-10_38_07
Theory : euclidean!plane!geometry
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