Nuprl Lemma : geo-cong-preserves-gt-prim
∀e:EuclideanPlane. ∀a,b,c,d,x,y:Point. (ab ≅ cd ⇒ cd>xy ⇒ ab>xy)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
euclidean-plane: EuclideanPlane,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
geo-ge: ab ≥ cd,
guard: {T},
uimplies: b supposing a
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d,x,y:Point. (ab \mcong{} cd {}\mRightarrow{} cd>xy {}\mRightarrow{} ab>xy)
Date html generated:
2020_05_20-AM-09_44_40
Last ObjectModification:
2020_01_27-PM-11_03_26
Theory : euclidean!plane!geometry
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