Nuprl Lemma : geo-gt-implies-geo-gt-prim
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab > cd ⇒ ab>cd)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
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],
implies: P ⇒ Q,
geo-gt: cd > ab,
squash: ↓T,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geo-axioms: BasicGeometryAxioms(g),
cand: A c∧ B,
geo-ge: ab ≥ cd,
not: ¬A,
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd),
or: P ∨ Q,
false: False
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab > cd {}\mRightarrow{} ab>cd)
Date html generated:
2020_05_20-AM-09_45_05
Last ObjectModification:
2020_01_13-PM-05_09_50
Theory : euclidean!plane!geometry
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