Nuprl Lemma : eu-eq_dist-axiomsB
∀g:EuclideanPlane. ((∀a,b,c:Point. (a # bc ⇒ |ac| < |ab| + |bc|)) ⇒ dist-axiomsB(g))
Proof
Definitions occuring in Statement :
dist-axiomsB: dist-axiomsB(g),
geo-lt: p < q,
geo-add-length: p + q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
dist-axiomsB: dist-axiomsB(g),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
basic-geometry-: BasicGeometry-,
dist: D(a;b;c;d;e;f),
cand: A c∧ B,
exists: ∃x:A. B[x],
not: ¬A,
false: False,
or: P ∨ Q,
stable: Stable{P},
uiff: uiff(P;Q),
geo-eq: a ≡ b,
squash: ↓T,
true: True,
dist-tri: Dtri(g;a;b;c)
Latex:
\mforall{}g:EuclideanPlane. ((\mforall{}a,b,c:Point. (a \# bc {}\mRightarrow{} |ac| < |ab| + |bc|)) {}\mRightarrow{} dist-axiomsB(g))
Date html generated:
2020_05_20-AM-10_49_29
Last ObjectModification:
2020_01_13-PM-06_35_20
Theory : euclidean!plane!geometry
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