Nuprl Lemma : dist-to-gt
∀g:EuclideanPlane. ∀a,b,c,d:Point. (D(a;b;b;b;c;d) ⇒ ab > cd)
Proof
Definitions occuring in Statement :
dist: D(a;b;c;d;e;f),
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
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],
euclidean-plane: EuclideanPlane,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
dist: D(a;b;c;d;e;f),
geo-gt: cd > ab,
exists: ∃x:A. B[x],
and: P ∧ Q,
squash: ↓T,
basic-geometry: BasicGeometry,
sq_stable: SqStable(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
cand: A c∧ B
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d:Point. (D(a;b;b;b;c;d) {}\mRightarrow{} ab > cd)
Date html generated:
2020_05_20-AM-10_48_15
Last ObjectModification:
2020_01_13-PM-06_04_53
Theory : euclidean!plane!geometry
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