Nuprl Lemma : dist-lemma-lt
∀g:EuclideanPlane. ∀a,b,c,d,e,f:Point. (D(a;b;c;d;e;f) ⇒ |ef| < |ab| + |cd|)
Proof
Definitions occuring in Statement :
dist: D(a;b;c;d;e;f),
geo-lt: p < q,
geo-add-length: p + q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
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,
geo-lt: p < q,
dist: D(a;b;c;d;e;f),
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
basic-geometry: BasicGeometry,
guard: {T},
uimplies: b supposing a,
true: True,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d,e,f:Point. (D(a;b;c;d;e;f) {}\mRightarrow{} |ef| < |ab| + |cd|)
Date html generated:
2020_05_20-AM-10_47_58
Last ObjectModification:
2020_01_13-PM-06_04_35
Theory : euclidean!plane!geometry
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