Nuprl Lemma : geo-le-iff
∀e:BasicGeometry. ∀A,B,C,P:Point. (|AB| ≤ |CP| ⇐⇒ CP ≥ AB)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length: |s|,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-ge: ab ≥ cd,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
geo-le: p ≤ q,
squash: ↓T,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
or: P ∨ Q,
geo-ge: ab ≥ cd,
not: ¬A,
false: False,
stable: Stable{P},
geo-eq: a ≡ b,
uiff: uiff(P;Q),
true: True,
geo-between: B(abc),
cand: A c∧ B,
geo-length: |s|,
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)
Latex:
\mforall{}e:BasicGeometry. \mforall{}A,B,C,P:Point. (|AB| \mleq{} |CP| \mLeftarrow{}{}\mRightarrow{} CP \mgeq{} AB)
Date html generated:
2020_05_20-AM-09_53_23
Last ObjectModification:
2020_01_28-AM-09_58_55
Theory : euclidean!plane!geometry
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