Nuprl Lemma : geo-not-gt-to-ge
∀g:EuclideanPlane. ∀x,y,e,f:Point. ((¬xy > ef) ⇒ ef ≥ xy)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
geo-ge: ab ≥ cd,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
false: False,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
stable: Stable{P},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
basic-geometry-: BasicGeometry-,
uiff: uiff(P;Q)
Latex:
\mforall{}g:EuclideanPlane. \mforall{}x,y,e,f:Point. ((\mneg{}xy > ef) {}\mRightarrow{} ef \mgeq{} xy)
Date html generated:
2020_05_20-AM-10_48_33
Last ObjectModification:
2020_01_13-PM-06_27_05
Theory : euclidean!plane!geometry
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