Nuprl Lemma : geo-gt-prim-implies-le
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab>cd ⇒ |cd| ≤ |ab|)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-le: p ≤ q,
geo-sep: a # b,
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
exists: ∃x:A. B[x],
uiff: uiff(P;Q),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
geo-length-type: Length,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
respects-equality: respects-equality(S;T),
or: P ∨ Q,
not: ¬A,
false: False,
stable: Stable{P},
geo-eq: a ≡ b,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
basic-geo-axioms: BasicGeometryAxioms(g)
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab>cd {}\mRightarrow{} |cd| \mleq{} |ab|)
Date html generated:
2020_05_20-AM-10_00_38
Last ObjectModification:
2020_01_28-AM-00_10_35
Theory : euclidean!plane!geometry
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