Nuprl Lemma : geo-add-length-property3
∀g:EuclideanPlane. ∀p,q:{p:Point| B(OXp)} . (B(Xpq) ⇒ p + |pq| ≡ q)
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length: |s|,
geo-mk-seg: ab,
geo-X: X,
geo-O: O,
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]}
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,
guard: {T},
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
prop: ℙ,
geo-add-length: p + q,
so_lambda: λ2x.t[x],
so_apply: x[s],
basic-geometry: BasicGeometry,
and: P ∧ Q,
sq_stable: SqStable(P),
squash: ↓T,
uiff: uiff(P;Q),
basic-geometry-: BasicGeometry-
Latex:
\mforall{}g:EuclideanPlane. \mforall{}p,q:\{p:Point| B(OXp)\} . (B(Xpq) {}\mRightarrow{} p + |pq| \mequiv{} q)
Date html generated:
2020_05_20-AM-09_59_34
Last ObjectModification:
2020_01_13-PM-03_44_06
Theory : euclidean!plane!geometry
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