Nuprl Lemma : geo-lt-lengths-to-sep
∀e:EuclideanPlane. ∀a,b,c:Point. (|ab| < |ac| ⇒ b # c)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
or: P ∨ Q,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
guard: {T},
uimplies: b supposing a,
geo-gt: cd > ab,
squash: ↓T,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
and: P ∧ Q,
not: ¬A,
basic-geometry-: BasicGeometry-,
geo-eq: a ≡ b,
false: False,
geo-length-type: Length,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
geo-length: |s|,
top: Top,
true: True,
iff: P ⇐⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
stable: Stable{P},
geo-zero-length: 0,
oriented-plane: OrientedPlane
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (|ab| < |ac| {}\mRightarrow{} b \# c)
Date html generated:
2020_05_20-AM-10_41_58
Last ObjectModification:
2020_01_27-PM-09_59_10
Theory : euclidean!plane!geometry
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