Nuprl Lemma : geo-add-length-between-iff
∀e:BasicGeometry. ∀[a,b,c:Point]. uiff(B(abc);|ac| = |ab| + |bc| ∈ Length)
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-between: B(abc),
geo-point: Point,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
geo-between: B(abc),
not: ¬A,
implies: P ⇒ Q,
false: False,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
geo-strict-between: a-b-c,
cand: A c∧ B,
squash: ↓T,
true: True
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b,c:Point]. uiff(B(abc);|ac| = |ab| + |bc|)
Date html generated:
2020_05_20-AM-09_53_44
Last ObjectModification:
2020_01_13-PM-03_24_05
Theory : euclidean!plane!geometry
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